# How do I solve the following problem?Juan jogs a certain distance and then walks a certain distance. When he jogs he averages seven milesper hour. When he walks, he averages 3.5 miles per hour. If...

How do I solve the following problem?

Juan jogs a certain distance and then walks a certain distance. When he jogs he averages seven milesper hour. When he walks, he averages 3.5 miles per hour. If he walks and jogs a total of six miles in a total of seven hours, how far does he walk?

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

You should come up with the notation x that expresses the time for walking, hence the time for jogging is 7 - x.

You need to remember the formula that expresses the distance in terms of speed and time such that:

distance = speed * time

The problem provides the information that Juan walks and jogs a total of 6 miles in 7 hours such that:

`3.5x + 7(7 - x) = 6`

You need to open the brackets such that:

`3.5x +49 - 7x = 6`

`-3.5x = 6 - 49 =gt -3.5x = -43`

`x = 43/3.5 =gt x~~ 12.28 `

You may find how far he walks multiplying 12.28 by 3.5 such that:

`d_1 = 12.28*3.5 `

`d_1 = 43`  miles

Hence, evaluating the time he walks yields `x ~~ 12.28 ` and how far does he walk yields `d_1 = 43`  miles.

catd1115 | Middle School Teacher | (Level 3) Assistant Educator

Posted on

I don't see that either poster has the correct answer. Sciencesolve's post seems good, and is very logical, but the answer cannot be correct because the question says he travels 6 miles TOTAL. etotheeyepi's answer by solving the system of equations also seems logical but does not yield a result. Is there anyone out there who can solve this? Can enotes reopen this question to answers? Or it is an unsolvable problem that needs to changed and if so any suggestion on how to change it so it works? Thanks!

etotheeyepi | Student, Undergraduate | (Level 1) Valedictorian

Posted on

j = jog time

w = walk time

j + w = 7

7j + 3.5w = 6

7j + 7w    = 49

- 3.5w = - 43

w = 12.3 mph

j = - 5.3 mph

7(-5.3) + 3.5(12.3) = 5.95

I think this problem has no solution, except for the possibilty that Jaun jogs bacwards faster than the walks.