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.

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proz proz · Answer 1 · 2020-09-18T03:00:14+02:00

Answer:

It took 1.2 hours to get to the store

Step-by-step 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:

[tex]speed = \frac{distance}{time} \\s = \frac{d}{t_1} \\t_1 = \frac{d}{s_1}\\t_1 =\frac{d}{4} - - - - - (1)[/tex]

Back from the store:

[tex]s_2 = \frac{d}{t_2} \\t_2 = \frac{d}{s_2}\\where:\\s_2 = 6\ miles\ per\ hour\\t_2 = \frac{d}{6} - - - - - - (2)[/tex]

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

t₁ + t₂ = eqn (1) + eqn (2)

[tex]\frac{d}{4} + \frac{d}{6} = 2\\Multiplying\ through\ by\ 12:\\3d\ +\ 2d\ =\ 24\\5d = 24\\d = \frac{24}{5} \\d = 4.8\ miles[/tex]

∴ length of trip to the store = t₁

from eqn (1)

[tex]t_1 = \frac{d}{4} \\t_1 = \frac{4.8}{4} \\t_1 = 1.2\ hours[/tex]