Measurement Word Problems
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Question 1 of 6
1. Question
Two trucks leave the centre of the city at the same time. One truck travels east and the other travels west. The eastbound truck travels at `65`km/h and the westbound truck at `58`km/h. When will the trucks be `553 1/2`km apart?Hint
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A word problem can be drawn as a diagram and then translated into an equation for easier solving.First, draw a diagram of the problem to understand it more
Translate the problem into an equation based on the diagramtime taken in hours: `t`distance of westbound truck: `58t`distance of eastbound truck: `65t`Distance West `+` Distance East `=` `553 1/2` `58t+65t` `=` `553 1/2` Since `S=d/t`, it means that `d=Sxxt`.Solve for `t``58t+65t` `=` `553 1/2` `123t` `=` `553 1/2` `123t``-:123` `=` `553 1/2``-:123` Divide both sides by `123` `t` `=` `4 1/2` hours `4 1/2` hours -
Question 2 of 6
2. Question
A lioness is `128` metres from a gazelle. The lioness starts to sprint towards the gazelle at `22`m/s. At the same time, the gazelle starts to sprint at `18`m/s. When will the lioness catch the gazelle?- (32) seconds
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A word problem can be drawn as a diagram and then translated into an equation for easier solving.First, draw a diagram of the problem to understand it more
Translate the problem into an equation based on the diagramNote that the gazelle and lioness would meet when their distance becomes equaltime taken in seconds: `t`distance of the gazelle: `128+18t`distance of the lioness: `22t`speed of the gazelle: `18\text(m/s)`speed of the lioness: `22\text(m/s)``\text(distance of the gazelle)` `=` `\text(distance of the lioness)` `128+18t` `=` `22t` Solve for `t``128+18t` `=` `22t` `128+18t` `-18t` `=` `22t` `-18t` Subtract `18t` from both sides `128` `=` `4t` `4t` `=` `128` `4t``-:4` `=` `128``-:4` Divide both sides by `4` `t` `=` `32` seconds `32` seconds -
Question 3 of 6
3. Question
Two submarines `55`km apart aimed and fired their torpedoes toward each other. Torpedo A averages `50`km/h and Torpedo B averages a speed of `60`km/h. When and where do they collide and impact each other?Hint
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A word problem can be drawn as a diagram and then translated into an equation for easier solving.First, draw a diagram of the problem to understand it more
Translate the problem into an equation based on the diagramtime taken in hours: `t`distance of Torpedo A: `50t`distance of Torpedo B: `60t`Distance A + Distance B: `55km``50t+60t` `=` `55` Since `S=d/t`, it means that `d=Sxxt`.Solve for `t``50t+60t` `=` `55` `110t` `=` `55` `100t``-:110` `=` `55``-:110` Divide both sides by `110` `t` `=` `1/2` hour or `30` minutes `30` minutes -
Question 4 of 6
4. Question
Two cars left Town A for Town B. The first car left at `8`am and averaged `100`km/h. The second car left at `9`am and averaged `120`km/h. At what time did they meet?Hint
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A word problem can be drawn as a diagram and then translated into an equation for easier solving.First, draw a diagram of the problem to understand it more
Translate the problem into an equation based on the diagramNote that the two cars would meet when their distance becomes equalhours that it will take for them to meet: `x`distance of first car: `100+100x` (this car left an hour earlier, because of its speed, it has a `100`km advantage)distance of second car: `120x``\text(distance of first car)` `=` `\text(distance of second car)` `100+100x` `=` `120x` Since `S=d/t`, it means that `d=Sxxt`. Let time `t=x` so we can have `d=Sxxx`.Solve for `x``100+100x` `=` `120x` `100+100x` `-100x` `=` `120x` `-100x` Subtract `100x` from both sides `100` `=` `20x` `20x` `=` `100` `20x``-:20` `=` `100``-:20` Divide both sides by `20` `x` `=` `5` hours `5` hours added to `9`am is `2`pm.Therefore, the two cars met at `2` pm`2`pm -
Question 5 of 6
5. Question
A pipe is `4.8` metres long. It is cut into three pieces. One piece is twice the length of the shortest piece. The other piece is `60`cm longer than the shortest piece. Calculate the length of each piece in centimetres.Hint
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A word problem can be drawn as a diagram and then translated into an equation for easier solving.First, draw a diagram of the problem to understand it moreshortest piece: `x`twice the shortest: `2x``60`cm longer than the shortest: `x+60`
Translate the problem into an equation based on the diagram, then make sure all units are in centimetres`x` `+``2x` `+(``x+60`cm`)` `=` `4.8`m `x` `+``2x` `+(``x+60`cm`)` `=` `480`cm Solve for `x``x` `+``2x` `+(``x+60`cm`)` `=` `480`cm `4x+60` `=` `480` `4x+60` `-60` `=` `480` `-60` Subtract `60` from both sides `4x` `=` `420` `4x``-:4` `=` `420``-:4` Divide both sides by `4` `x` `=` `105` Solve for `2x``2x` `=` `2(105)` Substitute `x` `=` `210` Solve for `x+60``x+60` `=` `105+60` Substitute `x` `=` `165` `105,165,210` -
Question 6 of 6
6. Question
The body of a lamp post is twice as long as its base. Its base is twice as long as its head. Altogether, the lamp post is `560`cm tall. How tall is each section?-
Head: (80)cmBase: (160)cmBody: (320)cm
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A word problem can be drawn as a diagram and then translated into an equation for easier solving.First, draw a diagram of the problem to understand it moreHead: `x`Base: `2x`Body: `4x`
Translate the problem into an equation based on the diagram`x+2x+4x` `=` `560`cm Solve for `x``x+2x+4x` `=` `560`cm `7x` `=` `560` `7x``-:7` `=` `560``-:7` Divide both sides by `7` `x` `=` `80`cm height of the head Solve for `2x``2x` `=` `2(80)` Substitute `x` `=` `160`cm height of the base Solve for `4x``4x` `=` `4(80)` Substitute `x` `=` `320`cm height of the body Head: `80`cmBase: `160`cmBody: `320`cm -