Question

Mr. Monasterio ran to the store for burritos at 4 miles per hour. On the way back, he increased his speed to 6 miles per hour. If the whole trip took 2 hours, how long was the trip to the store? Put your answer in decimal form.

Answer 1

It took 1.2 hours to get to the store

Explanation:

Let the time taken to reach the store be t₁

Let the time taken to come back be t₂

Let the speed to and from store = s₁ and s₂ respectively

let the distance to the store = d

To the store:

`speed = (distance)/(time) \\s = (d)/(t_1) \\t_1 = (d)/(s_1)\\t_1 =(d)/(4) - - - - - (1)`

Back from the store:

`s_2 = (d)/(t_2) \\t_2 = (d)/(s_2)\\where:\\s_2 = 6\ miles\ per\ hour\\t_2 = (d)/(6) - - - - - - (2)`

We are told that total time (t₁ + t₂) = 2 hours

t₁ + t₂ = eqn (1) + eqn (2)

`(d)/(4) + (d)/(6) = 2\\Multiplying\ through\ by\ 12:\\3d\ +\ 2d\ =\ 24\\5d = 24\\d = (24)/(5) \\d = 4.8\ miles`

∴ length of trip to the store = t₁

from eqn (1)

`t_1 = (d)/(4) \\t_1 = (4.8)/(4) \\t_1 = 1.2\ hours`