rvinodhini wrote:

Andy starts his journey from A to B and Ben starts his journey from B to A at the same time.After passing each other they complete their journeys in 3 1/3 and 4 4/5 hours respectively.Find the speed of Ben if Andy traveled at 12 miles/hr.

a) 8.33 m/hr

b) 10 m/hr

c) 22 m/hr

d) 20 m/hr

e)16.66 m/hr

Suppose Andy and Ben meet at point C. Then we have this diagram:

A---------------C-------------B

Now Andy goes from C to B at 12 mph, and it takes him 10/3 hours, so the distance from C to B is (12)(10/3) = 40 miles. Let's call the distance from A to C 'd'. Then we have:

A--------d-------C-------40------B

Now we know two things. The time it took Andy to travel d miles is the same as the time it takes Ben to travel 40 miles (since they traveled the same amount of time before meeting). If Ben's speed is s, then we know (since time = distance/speed) that

40/s = d/12

480 = sd

Further, we know that it took 24/5 hours for Ben to travel d miles, so

s = d/(24/5)

24s/5 = d

Now substituting this expression for d into the equation above

480 = s * (24s/5)

5*480/24 = s^2

100 = s^2

10 = s

There may well be a faster approach - this is just what I saw to do first.

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