Question

If a train runs at 40kmph it reaches its destination late by 11 minutes. But if it runs at 50kmph it is late by 5 minutes only. Find the distance to be covered by the train.

Answer 1

Let the correct time to complete the journey be x min.
Distance covered in (x + 11) 
min.= Distance covered in (x + 5) min at 50 km/hr
∴ (x+11)60 * 40
= (x+5)60 * 50
=x = 19 min

Answer 2

$\textbf{Solution:}$


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. 


#thankyou ☺☺