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John traveled 80% of the way from Yellow-town to

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Senior Manager
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John traveled 80% of the way from Yellow-town to [#permalink] New post 05 Apr 2006, 00:49
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John traveled 80% of the way from Yellow-town to Green-fields by train at an average speed of 80 miles per hour. The rest of the way John traveled by car at an average speed of v miles per hour. If the average speed for the entire trip was 60 miles per hour, what is v in miles per hour?

(a) 30
(b) 40
(c) 50
(d) 55
(e) 70
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 [#permalink] New post 05 Apr 2006, 01:29
The average speed for the entire trip= Total distance/Total time

60/60=D/T

D/T=1

Pick 100 km for D...
This would yield T=100 minutes

Using the question stem we calculate 80 km were traveled in 1h (or 60 minutes)....

This leaves us with 40 minutes (2/3 of an hour) to travel 20km.....

R*T=D

R*2/3=20

R=30

Answer A....
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 [#permalink] New post 05 Apr 2006, 09:55
A.

Let "100" be the total distance travel (D). Thus, D1 = 80 and D2 = 20.
V1 = 80 mph, V2 is the unknown, and total velocity (V) = 60 mph.

D1/V1 + D2/V2 = D/V

80/80 + 20/V2 = 100/60

20/V2 = 2/3

20 (3/2) = V2

30 = V2
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 [#permalink] New post 06 Apr 2006, 00:11
let total distance be d

First part by train took 0.8d/80 = 0.01 hour
Last part of journey took 0.2d/v hours

average speed = 80dv/(0.8vd + 16d) = 60
80vd = 48vd + 960d
32vd = 960
vd = 30d
v = 30
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 [#permalink] New post 06 Apr 2006, 07:13
A 30 m/hr

if we consider total distance to be x and time taken as t.

(0.8x/80)+(0.2x)/v = (x/60)
=> v = 30
  [#permalink] 06 Apr 2006, 07:13
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