Amar and Akbar left Bhubaneshwar simultaneously and travelled towards Cuttack. Amar's speed was 15 km/h and that of Akbar was 12 km/h. Half an hour later, Anthony left Bhubaneshwar and travelled in the same direction. Sometime later, he overtook Akbar and 90 minutes further on he overtook Amar. Find Anthony's speed. Amar and Akbar left Bhubaneshwar simultaneously and travelled towards Cuttack. Amar's speed was 15 km/h and that of Akbar was 12 km/h. Half an hour later, Anthony left Bhubaneshwar and travelled in the same direction. Sometime later, he overtook Akbar and 90 minutes further on he overtook Amar. Find Anthony's speed.
Answers
Answer:
Speed of anthony = 18 km/hr
Step-by-step explanation:
Amar and Akbar left Bhubaneshwar simultaneously and travelled towards Cuttack. Amar's speed was 15 km/h and that of Akbar was 12 km/h. Half an hour later, Anthony left Bhubaneshwar and travelled in the same direction. Sometime later, he overtook Akbar and 90 minutes further on he overtook Amar.
Amar speed = 15 km/hr
Akbar speed = 12 km/Hr
Anothny speed = A km/hr
Let say after t hrs he over took Akbar
Distance covered by Anthony = tA km
Distance covered by Akbar = (t + 1/2) 12 = 12t + 6 km
tA = 12t + 6
=> t = 6/(A -12)
Further 90 mins = 3/2 hrs he over took Amar
Distance covered by Amar = 15(t + 1/2 + 3/2) = 15t + 30 km
Distance covered by Anthony = (t + 3/2)A = tA + 3A/2 km
tA + 3A/2 = 15t + 30
=> t (A -15) = 30- 3A/2
=> t = (60-3A)/(2(A-15))
Equating t
6/(A -12) = (60-3A)/(2(A-15))
=> 12 A - 180 = -3A² + 96A - 720
=> 3A² - 84A + 540 = 0
=> A² -28A + 180 = 0
=> A² - 18A - 10A + 180 = 0
=> A(A-18) -10(A -18) =0
=> (A-10)(A-18) = 0
A = 10 or 18
Anthony speed is more than Amar & akbar so
A = 18
Speed of anthony = 18 km/hr
Amar and Akbar left Bhubaneshwar simultaneously and travelled towards Cuttack. Amar's speed was 15 km/h and that of Akbar was 12 km/h. Half an hour later, Anthony left Bhubaneshwar and travelled in the same direction. Sometime later, he overtook Akbar and 90 minutes further on he overtook Amar. Find Anthony's speed. Amar and Akbar left Bhubaneshwar simultaneously and travelled towards Cuttack. Amar's speed was 15 km/h and that of Akbar was 12 km/h. Half an hour later, Anthony left Bhubaneshwar and travelled in the same direction. Sometime later, he overtook Akbar and 90 minutes further on he overtook Amar. Find Anthony's speed.
