Abe and Amil rode in a bike-a-thon. Abe rode for 77 minutes at a faster rate per mile than Amil. Find Amil's unit rate. Then explain how you could use it to find a possible unit rate for Abe. Amil rode 15 miles in 55 minutes.

Step-by-step explanation:
If Abe rode for 77mins
Let ta represent Amil time and tb represent Abe time.
Then tb=77mins
The rate if amil is faster than able
Let the speed of mail be Va and that of Abel be Vb
Therefore Va>Vb
Velocity = distance / time
Amil rate Va=d/ta
If Amil rode 15miles
Da = 15miles
ta= 55mins
Since they are on the same track then the rate of Amil is
Va=Da/ta
Va= 15/55
Va= 0.273miles/minutes
Since they are on the same track they will have the same speed Da.
Vb= 15/77
Vb= 0.195miles/minutes

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The answer to that is 6

Answer

1 number

explanation

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

 

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.