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 Post subject: Practice Test Rate QuestionPosted: Sat Aug 21, 2010 1:04 pm

Joined: Sun Jul 25, 2010 12:56 pm
Posts: 1
Hi, A practice test recently had the following question and I still don't understand the solution explanation given. Can anyone assist?

At 1:00, Jack starts to bicycle along a 60 mile road at a constant speed of 15 mph. Thirty minutes earlier, Scott started bicycling toward Jack on the same road at a constant speed of 12 mph. At what time will they meet?

A: 1:30
B: 3:00
C: 5:00
D: 6:00
E: 9:00

I would imagine we combine their speeds in order to solve, but the explanation doesn't offer this solution. Any insight would be welcome.

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 Post subject: Re: Practice Test Rate QuestionPosted: Tue Aug 24, 2010 2:20 pm

Joined: Thu Jul 03, 2008 2:13 pm
Posts: 117
Hey Raya,

Good question - you can do this one a couple of ways. My personal preference has always been:

Use two equations for Rate = Distance/Time (one for each person/car/train) and then consolidate your D and T variables, which always have a relationship. Here:

Scott travels for 1/2 hour more than Jack, so his time could be T + 1/2 if Jack's is T
If we call Scott's distance D, then Jack's is 60 - D, since both distances have to add to 60.

You'd then have:

R(Jack) = 15 = D/T
R(Scott) = 12 = (60-D)/(T+1/2)

If we sub the first equation into the second (the first can be expressed as D = 15T, and we can then put 15T in for D in the second), we'd have:

12 = (60 - 15T)/(T + 1/2)
12T + 6 = 60 - 15T
27T = 54
T = 2 hours

If they meet after 2 hours, then they meet at 3:00.

Even though it can be slightly more time consuming, I like this method because it works for pretty much any rate/distance/work problem, so it's a one-stop shop.

To use the additive rates property on this one, you'd need to account for the fact that they're only working together for part of the 60 mile route, because Scott rides alone for 30 minutes. So you'd first need to figure out how far Scott goes in 30 minutes:

R = D/T
12 = D/(1/2)
6 = D, so Scott goes 6 miles

Then we can combine rates to see how long it takes them, together, to travel the 60-6 = 54 miles remaining.

Combined rate = 12 + 15 = 27 miles/hour
R = D/T
27 = 54/T
27T = 54
T = 54/27 = 2 hours

Again, we get 2 hours past the 1:00 start time, so the answer is B.

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