Question

A challenged B to participate in a marathon and also gave B a lead of 63 km. Speed of A is 13/4 times than the speed of B. Find the total distance of the marathon if both of A and B reached the victory post at the same time.
1. 91 km
2. 88 km
3. 93 km
4. 85 km
5. 96 km

Answer 1

Correct Answer - Option 1 : 91 km

Given:

Speed of A = 13/4 times the speed of B

A gave B the lead of 63 km

Total time taken by A = Total time taken by B

Concept used:

Distance = Time × Speed

Calculation:

Let speed of B = 4 km/hr

Speed of A = (13/4) × 4

⇒ Speed of A = 13 km/hr

Let the distance covered by B after 63 km be x

⇒ Time taken to cover x km = x/4 hr     ----(i)

Now, Total distance covered by A = (63 + x) km

⇒ Time taken by A to cover (63 + x) km = (63 + x)/13      ----(ii)

Now, we know time taken by A = Time taken by B

So, (63 + x)/13 = x/4

⇒ 13x = 4x + 252

⇒ 9x = 252

⇒ x = 28 km

Now, total distance of marathon = 63 + 28

⇒ Total distance of marathon = 91 km