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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Answered by
529
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
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
thanx n u r welcom
Answered by
152
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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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).
-------------------------------------------------------------------------------------------------
Request: This forum is for helping those who actually need help. Do not make this a testing ground. Everybody here is humbly and willingly helping without looking for rewards.
So please, post only those questions which you really do not understand.
you may also post a solution you have for a question but do not understand certain step or steps in the solution.
I really do not know the solution.
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