A cyclist bikes x distance at 10 miles per hour and returns over the same path at 8 miles per hour. What is the cyclist's average rate for the round trip in miles per hour? ( please help me ! )
w=d/t
let x=80, so
(80+80)/(8hs+10hrs)
=8.8889 mi/hour
I don't know why nancy picked 80 as a value for x, since it could be almost any value.
Since the distance is the same for both rates, it the mean of 10 and 8.
(10 + 8)/2 = 9
To find the cyclist's average rate for the round trip, we can use the formula:
Average Speed = Total Distance / Total Time
Let's calculate the total distance first.
The first leg of the trip (going) is x miles at a speed of 10 miles per hour. So the time taken for this leg is:
Time1 = Distance1 / Speed1 = x / 10
The second leg of the trip (returning) is also x miles, but at a speed of 8 miles per hour. So the time taken for this leg is:
Time2 = Distance2 / Speed2 = x / 8
The total distance for the round trip is x + x = 2x miles.
The total time for the round trip is the sum of the time taken for the going and returning legs:
Total Time = Time1 + Time2 = x/10 + x/8
Now, we can substitute the values into the formula for average speed:
Average Speed = Total Distance / Total Time
Average Speed = 2x / (x/10 + x/8)
To simplify this, we need to find a common denominator for x/10 and x/8, which is 40:
Average Speed = 2x / (4x/40 + 5x/40)
Now we can add the fractions:
Average Speed = 2x / (9x/40)
To divide by a fraction, we multiply by its reciprocal:
Average Speed = 2x * (40 / 9x)
The x's cancel out:
Average Speed = 2 * 40 / 9
Average Speed = 80 / 9 miles per hour
Therefore, the cyclist's average rate for the round trip is approximately 8.89 miles per hour.