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

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.