   SEARCH HOME Math Central Quandaries & Queries  Subject: Word Problem Name: Maria Who are you: Student 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. At what speeds were they travelling? Can you please help me. I just don't have a clue where to start with these word problems. 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.>     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.