SOLUTION: 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

Question 1376: 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?
Found 2 solutions by khwang, melzaren:
Answer by khwang(438) (Show Source): You can put this solution on YOUR website!
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.
Answer by melzaren(3) (Show Source): You can put this solution on YOUR website!
Regrettably, Khwang's answer is wrong:
"Hence, his speed going to the fair was 4 miles/hr,and
his speed backing home was 8 miles/hr."
The question states that Antoine's total travel time was 3 hours. If he travelled even 1 hour at 4 miles/h or 8 miles/h he would exceed 3 hours of travelling time.
"Antoine rode his bike the 4 miles to the fair at a relaxed pace. "
trip to the fair:
4 miles @ a speed of x mph
"He stayed to long and had to double his speed on the way back in order to get home in time for dinner."
trip home:
4 miles @ a speed of 2x mph
The question states that the entire trip took three hours, so we will build an equation with = 3 hours on the right hand side.
Now we include the entire trip on the Left hand side of the equation. Since we're solving for time we flip the miles/h ratio to h/miles, so that the unit "miles" cancels and we're left with hours: We have an algebraic representation of the speed of the trip above.
4 miles * h/(x miles) + 4 miles * h/(2x miles) = 3 hours

miles cancels out:
4h/x + 4h/2x = 3h

Get the x out of the denominators by multiplying every term by 2x:
8h + 4h = 6hx
12h = 6hx

divide through by 6h
2 = x
Now we know the value of x, plug it in to the speed ratios above and you have your answer.

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