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| Math Central | Quandaries & Queries |
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Subject: Word Problem Kim and Julie are joining Nicole at her parents cottage for the weekend. The cottage is 150km away from their neighbourhood. Kim can leave directly after school but Julie will be leaving after band practice, an hour and a quarter later. Kim took her time and drove slowly, averaging 20km/h slower than Julie. They both arrived at the same time. |
Hi Maria.
The main formula is distance = speed x time.
The distance is the same for Kim and Julie (150 km).
Assign variables (letters) to the unknown quantities, then try to reduce the number of unknowns:
Let s = Kim's speed.
Let t = Kim's time.
Let S = Julie's speed.
Let T = Julie's time.
So:
150 = st and 150 = ST
That's four unknown quantities - can we reduce this with more information? yes. We know that Kim's speed is Julie's speed minus 20:
s = S - 20, so substitute this for s:
(S - 20)t = 150
We also know that Kim spend an extra hour and a quarter driving, so t = T + 5/4
(S - 20)(T + 5/4) = 150
That's two unknowns. Can we get down to one? yes. Because if 150 = ST, then T = 150/S, so
(S - 20) ( 150/S + 5/4) = 150
Now you have one equation with one unknown in it. Can you solve it from here?
Stephen La Rocque.>
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