Lindsey started biking to the park traveling 15 mph, after some time the bike got a flat so Lindsey walked the rest of the way, traveling 4 mph. If the total trip to the park took 5 hours and it was 53 miles away, how long did Lindsey travel at each speed
Answer:
Lindsey biked 45 miles for 3 hours at 15 mph and walked 8 miles for 2 hours at 4 mph.
Explanation:
Speed = distance/time
Let the distance that Lindsey biked through be x miles and the time it took her to bike through that distance be t hours
Then, the rest of the distance that she walked is (53 – x) miles
And the time she spent walking that distance = (5 – t) hours
Her biking speed = 15 mph = 15 miles/hour
Speed = distance/time
15 = x/t
x = 15 t (eqn 1)
Her walking speed = 4 mph = 4 miles/hour
4 = (53 – x)/(5 – t)
53 – x = 4 (5 – t)
53 – x = 20 – 4t (eqn 2)
Substitute for X in (eqn 2)
53 – 15t = 20 – 4t
15t – 4t = 53 – 20
11t = 33
t = 3 hours
x = 15t = 15 × 3 = 45 miles.
(53 – x) = 53 – 45 = 8 miles
(5 – t) = 5 – 3 = 2 hours
So, it becomes evident that Lindsey biked 45 miles for 3 hours at 15 mph and walked 8 miles for 2 hours at 4 mph.