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Question

A scooter travels 10 miles perhour faster than an electric bicycle. The scooter traveled for 3 hours, and the bicycle traveled for 5 1/2 hours. All together, the scooter and bicycle traveled nomore than 285 miles. Find the maximum speed of each.

Answer 1

Let S = Speed of the scooter and B = Speed of bicycle

Note that (miles/hour)(hours) = miles so find the distance by multuplying the spped by the time travelled

 

We have two equations:

 

S = B+10

3S + 5.5B <= 285

 

Substitute B+10 in place of S in 2nd equation

 

3(B+10) + 5.5B <= 285

 

3B + 30 + 5.5B <= 285

8.5B <= 285-30

8.5B <= 255

Divide out the coefficient giving

(8.5B)/8.5 <= 255/8.5

B <= 30

 

S = B+10 so

S <= 40

 

Scooter max 40 mph

Bicycle max 30 mph