Two horses started simultaneously towards each other and meet each other 3 hr 20 mins later. How much time will it take the slower horse to cover the whole distance if the first arrived at the place of departure of the second 5 hours later than the second arrived at the point of departure of the first?
A.10 hours
B.5 hours
C.15 hours
D.6 hours
Answers
Answer:
Ans: 10 hr
Step-by-step explanation:
Let distance between the two places =d km
Let total time taken by slower horse
= ( t + 5 ) hr,
total time taken by faster horse = t hr.
Therefore, speed of the slower horse = d t + 5 km/hr
speed of the faster horse
= d t km/hr
The two horses meet each other in 3 hour 20 min.
(i.e., in
3 1 3 hr = 10 3 hr)
In this time, total distance travelled by both the horses together is
d
.
Therefore,
dt + 5 × 10 3 + d t × 10 3 = d 10 3
( t + 5) + 10
3 t = 1 10 t + 10
( t + 5 ) = 3 t ( t + 5 )
20 t + 50 = 3
t 2 + 15 t 3
t 2 − 5 t − 50 = 0
2 + 10 t − 15 t − 50 = 0
t ( 3 t+ 10 ) − 5
( 3 t + 10) = 0
( 3 t + 10 )
( t − 5 ) = 0
t = 5
(ignoring -ve value)
i.e., total time taken by slower horse = 5 + 5 = 10 hr
Step-by-step explanation: