Charlie biked 15 minutes home from school and then walked 12 minutes to the pizza place near his house. This trip was 3.6 miles in total. His rate on his bike is 3 miles per hour less than 5 times his walking rate. In miles per hour, what is Charlie’s speed as he walks and what is his speed as he bikes?
+128464 Let the rate he walks = W
Then the rate he bikes = 5W - 3
Note that we need to convert minutes to hours :
15 min = 1/4 hr
12 min =1/5 hr
And note that
rate on bike * time + walking rate * time =total distance
So
(5W - 3) (1/4) + (W)(1/5) = 3.6 simplify
(5/4)W - 3/4 + (1/5)W = 3.6 { 5/4 = 1.25 , 3/4 = .75, 1/5 = .2 }
1.25W - .75 + .2W = 3.6
1.45W - .75 = 3.6 add .75 to both sides
1.45W = 4.35 divide both sides by 1.45
W = 3 mph = walking rate
Biking rate = 5(3) - 3 = 12 mph
