Pls help as soon as possible

Question

Dave walked to his friend's house at a rate of 4 mph and returned back biking at a rate of 10 mph. If it took him 18 minutes longer to walk than to bike, what was the total distance of the round trip?

Answer 1

So here we should recall that distance = time*speed. Because we don't know what the distance is, let's use a variable for now. Likewise with time.

Now, we can write out two equations, one for the trip there and one for the trip back. Before we write out the equations, however, it must be noted that the speed is given in miles per hour, while the time is in minutes. This is an easy way to get confused with units, so it would be better to turn the time into hours. 18 minutes is the same as saying 18/60 hours, or .3 hours.

d = 4 * (t + .3) Here, we set the time as t + .3 because the problem indicated that it took Dave 18 min, or .3 hours, as we found previously, longer to walk.

d = 10 * t

Because the distance there and back is the same, we set the two equal to each other.

4*(t + .3) = 10*t

4*t + 4*.3 = 10*t

4*t + 1.2 = 10*t

1.2 = 6*t

t = .2 hours

Now that we have found the time, we can now try to find the distance. Here we go back to the simpler of our two equations:

d = 10*t

d = 10*.2

d = 2 miles