It takes Mike 8 minutes to walk to the store from his house. The return trip takes 13 minutes because he walks 1mph slower due to the bags he is carrying. How fast did Mike walk on his way to the store? Carry out one decimal place.

Question

It takes Mike 8 minutes to walk to the store from his house. The return trip takes 13 minutes because he walks 1mph slower due to the bags he is carrying. How fast did Mike walk on his way to the store? Carry out one decimal place.

Thanks in advance!

Answer 1

rate going to store --- x mph

rate coming back ----- x-1 mph

(8/60)x = (13/60)(x-1)
times 60
8x = 13(x-1)
8x - 13x = -13
-5x = -13
x = 2.6

So he walked to the store at 2.6 mph

check:
(8/60)(2.6) = .34666...
(13/60)(1.6) = .34666... , ---> same distance

Answer 2

distance = speed*time, and the two distances are the same, so

8s = 13(s-1)
s = 13/5 = 2.6 mph

Note that we can mix minutes and mph, because the same factor would be applied to both sides if we converted everything to minutes or hours. As long as the units on both sides match, we are ok.

Answer 3

To find Mike's walking speed on his way to the store, we can use the formula:

Speed = Distance / Time

First, let's calculate the distance between Mike's house and the store. Since the distance will be the same for both the trip to the store and the return trip, we can calculate it using the time taken for either trip.

Since Mike takes 8 minutes to walk to the store, we can use this value to calculate the distance. However, we need to convert the time to hours (since speed is usually measured in miles per hour):

Time (in hours) = 8 minutes / 60 (minutes per hour) = 0.1333 hours

Now, let's calculate the distance:

Distance = Speed x Time

We'll use "d" to represent the distance:

d = Speed x 0.1333

For the return trip, Mike takes 13 minutes, which is equivalent to 0.217 hours. Since he walks 1 mph slower on the return trip, we can represent his speed on the return trip as "Speed - 1".

Now, let's calculate the distance for the return trip:

d = (Speed - 1) x 0.217

Since the distance is the same for both trips (d = d), we can set up an equation:

Speed x 0.1333 = (Speed - 1) x 0.217

Now, we can solve this equation to find Mike's walking speed on his way to the store.

0.1333Speed = 0.217(Speed - 1)

0.1333Speed = 0.217Speed - 0.217

0.1333Speed - 0.217Speed = -0.217

-0.0837Speed = -0.217

Speed ≈ -0.217 / -0.0837 ≈ 2.59

So, Mike's walking speed on his way to the store is approximately 2.59 mph.