speed distance and time

Question

A bicyclist was going from point A to point B with a speed of 12 km/h. On the way back he increased his speed to 18 km/h and covered the distance in 15 minutes less. What is the distance between point A and point B?

Answer 1

You have to be careful with this question because the the rate of speed is given in kilometers per HOUR while the time saved is given to us in MINUTES. So you'll have to convert the minutes to hours first. 15 minutes is the same thing as 15/60 hours or 0.25 Hours

 

Distance = Rate • Time

D = 12T

D = 18(T - 0.25)

 

Since both of these are equal to the same distance, we can set the two equations equal to each other

 

12T = 18(T - 0.25)

12T = 18T - 4.5

-6T = -4.5

T = 0.75

 

Now we have our time, so we should plug it back into one of the original equations to find Distance

 

D = 12T

D = 12(0.75)

D = 9

Answer 2

12t = 18(t - 1/4) ------> 15 mins = 1/4 hr

12t = 18t - 4 1/2

6t = 4 1/2

t = 9/2 x 1/6

t = 3/4

 

d = 12(3/4) = 9 km