Question

In a race, Alice and Brenda started at the same time and ran with constant spends of 12 km and 20 km per hour, respectively. If Alice crossed the finish line 1 minute after Brenda, how many kilometers long was the race?

Answer 1

@jim_thompson5910

Answer 2

Since it said "minute" somewhere in the problem, I thought of converting the 12km/hr and 20km/hr into minutes. But I am not sure if that's how I am supposed to start it or if that's even correct.

Answer 3

\[\frac{ 12 }{ 60 } = \frac{ 1km }{ 5minutes }\]
\[\frac{ 20 }{ 60 } = \frac{ 1 km }{ 3 minute }\]

Answer 4

A minute is 1/60 hr, right?
So
$$
(t+1/60)12=20t
$$
Solve for t then plug back in to find the total distance
t is in hours

Does this make sense

Answer 5

So I I just use your formula then I will get it correct?

Answer 6

12t + 1/5 = 20t
12t - 12t + 1/5 = 20t - 12t
1/5 = 8t
1/5 / 8 = 8t / 8
1/40 = t

Answer 7

looks good, now plug that into either side of the original equation to find the distance

20t is the easier side

Answer 8

20/40 = 1/2

Okay thanks :)

Answer 9

But how did @ybarrap make that equation?

Answer 10

he used d = r*t

d = distance
r = rate
t = time

Answer 11

Also, we are learning about the method called "Backsolving" so if you can help me with that on this problem.

Answer 12

on the left side

r = 12
t is t+1/60

on the right side

r = 20
t is just itself: t