the average speed of boat p andQ in still water 7 km/hr.both p can cover 71 km upstream in 14.2 hr while Q can cover 81 km upstream in 81 hrs.find the time taken boat p cover 234 km down stream?
Answers
Given :- The average speed of boat P and Q in still water 7 km/hr. P can cover 71 km upstream in 14.2 hr while Q can cover 81 km upstream in 81 hrs. find the time taken boat P cover 234 km down stream ?
Solution :-
→ (P + Q)/2 = 7
→ P + Q = 14 km/h .
Let speed of P is P km/h , so speed of Q is (14 - P) km/h .
also, let speed of stream is x km/h .
so,
→ 71/(P - x) = 14.2 = 14(1/5) = 71/5
→ (P - x) = 5 -------- Eqn.(1)
and,
→ 81/(14 - P - x) = 81
→ 14 - P - x = 1
→ P + x = 13 --------- Eqn.(2)
adding Eqn.(1) and Eqn.(2) ,
→ P + P + x - x = 5 + 13
→ 2P = 18
→ P = 9 km/h .
putting value of P in Eqn.(1),
→ 9 - x = 5
→ x = 9 - 5 = 4 km/h .
therefore,
→ The time taken boat P to cover 234 km downstream = D/S = 234/(9 + 4) = 18 Hours (Ans.)
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