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rate problem

Expert replies
by Gurpinder » Wed Jul 07, 2010 2:25 pm
1. Tyrone rides his bicycle 5 miles from his home to the city bus stop at
the rate of 8 miles per hour. He arrives in time to catch the bus to work,
which travels at 25 miles per hour. If he spends 1.5 hours traveling from
home to work, how far does he travel on the bus?

2. At what rate must Eden travel to overtake Rex, who is traveling at a rate
20 miles per hour slower than Eden, if Eden starts 2 hours after Rex and
wants to overtake him in 4 hours?

can you explain how to solve this problem and perhaps what is the best approach for rate problems
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Source: — Problem Solving |

by Rich@VeritasPrep » Wed Jul 07, 2010 3:35 pm
Hey Gurpinder,

Problem 1:

If Tyrone rides 5 mi at a rate of 8 mi/hr, he did so in 5/8 hr. You can get this by using the forumla d = r*t, where d is distance, r is rate (or speed), and t is time.

The total trip took 1.5 hours, which can be written as 12/8 hrs. So after the 5/8 hrs on his bike, he spends 7/8 hrs on the bus.

The bus travels at 25 mi/hr. Use d = r*t again:

d = (25)*(7/8) = 175/8 = 21.875 mi.
Rich Zwelling
GMAT Instructor, Veritas Prep
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by Rich@VeritasPrep » Wed Jul 07, 2010 3:42 pm
If Eden goes 20 mi/hr faster than Rex, then that means that Eden gains 20 miles on Rex in one hour.

If Eden wants to overtake Rex in 4 hours, that means he will go a total of 20*4 = 80 miles more than Rex.

That means that Rex is 80 miles ahead of Eden when Eden starts travelling.

One thing that's left ambiguous in this question is whether or not the two start at the same point, but I'm assuming that is what's implied here.

Since Rex traveled 80 miles in 2 hours, he was going 40 mi/hr. That means Eden must go 60 mi/hr.
Rich Zwelling
GMAT Instructor, Veritas Prep
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by Gurpinder » Wed Jul 07, 2010 4:50 pm
thank you raz. i get them now. i just needed a little practice.

= )
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