A distance of 600 km is to be covered using both Train & Bus. If first 120 km are covered by train and rest by Bus, it takes 8 hr in all. However if the train is used for 80 km more, it takes 20 min more for the entire journey. What is the speed of train?

(A) 40 mph
(B) 45 kmph
(C) 50 mph
(D) 60 mph
(E) 72 mph

(Try to arrive at the answer using an elegant solution)
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Karishma
Veritas Prep GMAT Instructor

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my method is conventional one:
given total distance is 600km

case 1 120 km by train and 480 km by bus = 8hr journey ; 480 mins
speed of train be x and speed of bus y
so
120/x+ 480/y = 480
120y+480x=480xy--(1)

case 2:
200 km by train and 400 km by bus = 500 mins
or say
200y+400x=500xy --(2)

solve for x & y
x= 1 km per min or 60 kmph
and y = 1.33 km per min or 80 kmph
IMO D is correct..
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Absolutely GMATinsight! This is what I had in mind!
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Karishma
Veritas Prep GMAT Instructor

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It helps me to transform the equations into 'smaller numbers'.
Since:
x = speed of train
y = speed of bus
Eq I :
120/x + 480/y = 480 (divide all by 60)
2/x + 8/y = 8
2y +8x =8xy

Eq II:
200/x + 400/y = 500 (divide all by 100)
2/x + 4/y = 5
2y + 4x = 5xy

Subtract II from I:
4x = 3xy
y = 4/3
and
x = 1 km/min = 60km/h

(Note:The answer choices should be in kph rather than mph.)

We see that the first distance by train is 120, and the second distance by bus is 480. Let r = the speed of the train, in mph, and let s = the speed of the bus, in mph. Thus, we have the equation for the time:

120/r + 480/s = 8

If the train is used for 80 km more, then it will travel for 120 + 80 = 200 km, and the bus will travel for 480 - 80 = 400 km. The additional 20 minutes for the trip brings the total time to 8 hours, 20 minutes, which is 8 + ⅓ hours, or 25/3 hours. Thus, we have:
200/r + 400/s = 8 + ⅓ = 25/3

Multiplying each of the equations by 3rs, we have:

360s + 1440r = 24rs (Eq. 1)

and

600s + 1200r = 25rs (Eq. 2)

Multiplying Eq. 1 by 5 and Eq. 2 by 3, we have;

1800s + 7200r = 120rs

and

1800s + 3600r = 75rs

Subtracting these two equations, we have:

3600r = 45rs

Dividing both sides by 45r, we have:

80 = s

Substituting this back to the very first equation, we have:

120/r + 480/80 = 8

120/r + 6 = 8

120/r = 2

r = 60

Answer: D
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