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speed problem

by GmatTakerNo.1 » Sat May 01, 2010 3:05 pm
Hey,

can anyone help me with this? What is the best approach to solve this question in 2 minutes?

Two truck drivers leave Frankfurt for Madrid along the same route. The first leaves at 8 am at average speed of 60 mph. The second leaves at 10am at an average speed of 75mph. What time will the second driver catch the first?

The answer is 6 pm.
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by Testluv » Sat May 01, 2010 4:45 pm
Where two objects are heading in opposite directions (usually 2 objects approaching each other) add the rates. Where, as here, two objects are heading in the same direction, subtract the rates. In other words, the rate at which the second object "catches up" to the first is just the difference in their 2 rates: 75 - 60 = 15mph. The first object travelled at a rate of 60mph for 2 hours before the second object departed. Thus, the first object has gained a "headstart" of 60*2 = 120 miles. This is the distance the second object must now close in order to catch up to the first.

speed = distance/time

time = distance/speed = 120/15 = 8 hours.

So, the second object will catch up to the first 8 hours after it (the second object) departs. 10am + 8 hours = 6pm.

Please always include the answer choices and source of the question.
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by pradeepkaushal9518 » Sat May 01, 2010 7:59 pm
how i solve the problem

lets at x distance both the trucks meets

t1 is time taken by truck with 60 mph to reach x distance so speed = distance by time
60 = x/t1
x=60t1
t2 is time taken by truck with 75 mph to reach x distance

75=x/t2 75t2=x

so 60t1=75t2
t2=t1-2
as second truck left after 2 hour of first so its time to reach x t2 should be less than 2 hours from first truck then only it can meet the point
solving we get t2 = 8 hours
it leaves the poit at 10 am so 10 am + 8 hrs = 6pm

i hope its help
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