I can walk at 6 km/h. I can ride my bike at 30 km/h. How far is the station from my house if I save 18 minutes by riding instead of walking?

Question

This is all the info I had. If you could help me work it out it would be helpful

Answer 1

Problems like this are best solved with the golden equation "d = rt," which stands for "distance = (rate)(time)"

 

Set up an equation for the walking situation. No one knows d or t right now, but we do know r. That's the speed, which is 6 km/h for walking.

 

d = 6t

 

Now set up an equation for biking. Again, we don't know d right now, but we do have r, and that's 30 km/h. We also kind of have t. We don't actually have t, but we know the biking situation takes 18 minutes less.

 

The speed is in kilometers per hour, so the the units for t has to be in hours. There are 60 minutes in an hour, so 18 minutes, in units of hours, is 18/60. That fraction can reduce to 3/10. Because biking takes 3/10 of an hour less, plug in (t - 3/10) for this equation.

 

d = 30(t - 3/10)

 

Look at our two equations side-by-side now.

 

d = 6t

d = 30(t - 3/10)

 

In both equations, d represents the distance between the station and the house. This means both d-terms are equal to each other. Because both the equations are equal to d, they are also equal to each other.

 

d = 6t

d = 30(t - 3/10)

6t = 30(t - 3/10)

 

From here, solve for t.

 

6t = 30(t - 3/10)

6t = 30t - 9

24t = 9

t = 3/8

 

The question's asking for the distance between the station and the house. Plug t = 3/8 back into any of the equations in the beginning to solve for d.

 

d = 6t

d = 6(3/8)

d = 18/8

d = 9/4

d = 2.25

 

This means that the distance between the two places is 2.25 kilometers. I hope this helps, and good luck with your math class!