Antoine rode his bike the 4 miles to the fair at a relaxed p

Antoine rode his bike the 4 miles to the fair at a relaxed pace. He stayed to long and had to double his speed on the way back in order to get home in time for dinner. If his total time traveling was 3 hours, how fast did he travel in each direction?

Solution

Let V be the speed of his going to the fair, then his speed of the return trip
was 2V.
Now the total distance of the round trip is 2*4 = 8 miles.
By Speed = Distance / Time , and so Time = Distance /SPeed,
we have 3 = 8/V + 8/(2V),
Cancel the denominator by multiple by 2, 6V = 16 + 8 = 24.
so, V =4 and 2V = 8.
Hence, his speed going to the fair was 4 miles/hr,and
his speed backing home was 8 miles/hr.