Anil started from city x at 10:00 am and travelled towards city y. After one hour sunil started from city y and traveled towards x. The total taken by anil and sunil for their journey are (k+2) hours and k hours respectively. They meet each other at 7:00 pm.The speed of the sunil is 7 km/ hour more then that of anil. Find the total time taken by anil for his journey
Answers
Answer:
18 hrs
Explanation:
Anil started from city x at 10:00 am
After one hour sunil started from city y => started at 11:00 am
Let say Speed of Anil = A km/Hr
Speed of Sunil = A + 7 km/hr
The total taken by anil and sunil for their journey are (k+2) hours and k hours respectively.
Distance of Journey for Anil = A * (k + 2) km
Distance of Journey for Sunil = (A + 7) k km
Ak + 2A = Ak + 7k
=> 2A = 7k
Distance of journey = (A + 7)(2A/7) = 2A²/7 + 2A
They meet at 7:00 PM Anil traveled till than for 9 Hrs
Sunil Traveled for 8 hrs
Distance by Anil = 9A km
Distance by Sunil = (A + 7)8 = 8A + 56 km
Total Distnace = 9A + 8A + 56 = 17A + 56 km
2A²/7 + 2A = 17A + 56
=>2A²/7 = 15A + 56
=> 2A² = 105A + 392
=> 2A²- 105A - 392 = 0
=> 2A² - 112A + 7A - 392 = 0
=> 2A(A - 56) + 7(A - 56) = 0
=> (2A + 7)(A - 56) = 0
=> A = 56
Speed of Anil = 56 km/hr
k = 2A/7 = 2 * 56/7 = 16
Time taken by Anil = 16 + 2 = 18 Hrs
Other information
Distance of total journey = 56 * 18 = 1008 km
Speed of sunil = 56 + 7 = 63 km
Time taken by sunil = 16 hrs
Distance traveled by Anil when they met = 9*56 = 504 km
Distance traveled by Sunil when they met 8*63 = 504 km