A man travels 370 km, partly by train and partly by car.
If he covers 250 km by train and the rest by car, it takes him 4 hours, but if he travels 130km by train and the rest by car he takes 18 min. longer. Find the speed of the train and car.

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Let the speed of the car be C kmph
Let the speed of the train be T kmph

4 hours = 250 km / T kmph + (370 - 250) km / C kmph

         4 = 250/T + 120/C  -- equation 1

4 hrs 18 minutes = 130 km / T kmph + (370 - 130)km / C kmph
       258/60 = 4.3 = 130 / T + 240 / C      --- equation 2

Multiply equation 1 by 2 and subtract equation 2 from it.

       8 - 4.3 = 500/T - 130/T + 240/C - 240/C

       3.7 = 370 / T

       T = 370/3.7 = 100 kmph

Substitute the value of T in equation 1 to get,

       4 = 250/T + 120/C  -- equation 1
       4 = 250/100 + 120/C
       4 - 2.5 = 120/C

       C = 120/1.5 = 80 kmph

The train runs at 100 kmph and the car runs at 80 kmph

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In the first case,let train and car travel 250 kms  and 120 kms in time t hrs and (4-t) hrs respectively.

In second case, train and car travel 130 kms and 240 kms in time (130/250)t hrs and (240/120)(4-t) hrs , i.e., in time (13/25)t hrs and 2x(4-t) hrs respectively as time taken is directly proportional to distance when speed remains the same.

Total time in second case is 4hrs18min or (43/10 hrs,
hence (13/25)xt + 2x(4-t) = 43/10
This gives t = 2.5 hrs (Verify yourself).
Hence speed of train and car is 100 km/h and 80 km/h respectively.(calculate from above data of distance traveled by train and car).
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