SOLUTION: if a train runs at 40 kmph it reaches its destination late by 11 minutes. but if it runs at 50 kmph it is late by 5 minutes only. find the distance to be covered by the train

Question 896107: if a train runs at 40 kmph it reaches its destination late by 11 minutes. but if it runs at 50 kmph it is late by 5 minutes only. find the distance to be covered by the train

Found 2 solutions by richwmiller, Theo:
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
40*(x+11/60)=50(x+5/60)
x = 19/60
40*30/60=20 km
50*24/60=20 km
The other tutor made the mistake of using 5 and 11 as hours not minutes. The train is going 40 and 50 km per hour not per minute
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let T equal the time that it should take.
let D = the distance.

rate * time = distance

you get:

40(T+11) = D

50(T+5) = D

since both expressions on the left side of the equation equal D, you can set these expressions equal to each other to get:

40(T+11) = 50(T+5)

simplify to get:

40T + 440 = 50T + 250

subtract 40T from both sides of the equation and subtract 250 from both sides of the equation to get:

440 - 250 = 50T - 40T

simplify to get:

190 = 10T

divide both sides of the equation by 10 to get:

T = 19

Solve for D in the first equation to get:

40(T+11) = D becomes 40(19+11) = D becomes 40(30) = D becomes 1200 = D

you get D = 1200

replace T with 19 and D with 1200 in the second equation to get:

50(T+5) = D becomes 50(19+5) = 1200 becomes 50(24) = 1200 becomes 1200 = 1200.

this confirms the solution is good for both equations.

T = 19 and D = 1200.

you are not asked to find T but you found it in the process of finding D.

the solution is that the distance to be covered by the trains is 1200 kilometers.

you could also have solved more directly for T as follows:

start with:

40(T+11) = D
50(T+5) = D

solve both of these equations for T to get:

T = (D - 440) / 40 and T = (D - 250) / 50

set these expressions equal to each other because they are both equal to T and you get:

(D - 440) / 40 = (D - 250) / 50

multiply both sides of this equation by 200 to get:

50 * (D - 440) = 40 * (D - 250)

simplify both sides of this equation to get:

50D - 50(440) = 40D - 40(250)

subtract 40D from both sides of this equation and add 50(440) to both sides of this equation to get:

50D - 40D = 50(440) - 40(250)

simplify to get 10D = 12000

divide both sides of this equation by 10 to get:

D = 1200 kilometers.

same answer only you didn't have to find the value of T first in order to get it.

Either way gets you the answer you are looking for which is that the distance each train has to cover is 1200 kilometers.
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