Let’s assume,
The speed of the train be x km/hr
The speed of the car = y km/hr
From the question, it’s understood that there are two parts
# Part 1: When Ramesh travels 160 Km by train and the rest by car.
# Part 2: When Ramesh travels 240 Km by train and the rest by car.
Part 1,
Time taken by Ramesh to travel 160 km by train = 160/x hrs [∵ time = distance/ speed]
Time taken by Ramesh to travel the remaining (760 – 160) km i.e., 600 km by car =600/y hrs
So, the total time taken by Ramesh to cover 760Km = 160/x hrs + 600/y hrs
It’s given that,
Total time taken for this journey = 8 hours
So, by equations its
160/x + 600/y = 8
20/x + 75/y = 1 [on dividing previous equation by 8] …………………… (i)
Part 2,
Time taken by Ramesh to travel 240 km by train = 240/x hrs
Time taken by Ramesh to travel (760 – 240) = 520 km by car = 520/y hrs
For this journey, it’s given that Ramesh will take a total of is 8 hours and 12 minutes to finish.
240/x + 520/y = 8 hrs 12 mins = 8 + (12/60) = 41/5 hr
240/x + 520/y = 41/5
6/x + 13/y = 41/200 ………. (ii)
Solving (i) and (ii), we get the required solution
Let’s take 1/x = u and 1/y = v,
So, (i) and (ii) becomes,
20u + 75v = 1 ……….. (iii)
6u + 13v = 41/200 ……. (iv)
On multiplying (iii) by 3 and (iv) by 10,
60u + 225v = 3
60u + 130v = 41/20
Subtracting the above two equations, we get
(225 – 130)v = 3 – 41/20
95v = 19/ 20
⇒ v = 19/ (20 x 95) = 1/100
⇒ y = 1/v = 100
Using v = 1/100 in (iii) to find v,
20u + 75(1/100) = 1
20u = 1 – 75/100
⇒ 20u = 25/100 = 1/4
⇒ u = 1/80
⇒ x = 1/u = 80
So, the speed of the train is 80 km/hr and the speed of car is 100 km/hr.