Pls help me.... Tq

Question

Faizal and Gary ran in a race. When Gary had completed the race, Faizal had only run 5/8 of the distance. Gary's speed was 75m/min faster than Faizal's speed. Both of them did not change their speeds throughout the race. What was Faizal's speed in m/min?

Answer 1

Look for some things that are equal in order to set up an equation.

The key here is that they both ran the same amount of time.

We know that D = RT, so T = D/R.

Find expressions for each of their times.

Let D = the total distance run by Gary (he completed the race)

Then (5/8)D is the distance run by Faizal.

Let F = rate at which Faizal ran the race.

Time for Gary is D / (F + 75), because Gary's speed/rate was 75 m/min faster than Faizal's.

Time for Faizal is (5/8) D / F

These times are equal:

D / (F + 75) = (5/8)D / F (you might want to write this down on paper with horizontal segments for the fractions. Cross multiply to reach:

DF = (5/8)D ( F + 75) , note that both sides are divisible by D

F = (5/8)(F + 75)

Multiply both sides by 8 to clear the fraction (would be my next step).

8F = 5(F + 75)

8F = 5F + 5(75)

3F = 5(75)

F = 5(25) = 125 m/min: this is Faizal's speed.

G = 200 m/min, this is Gary's speed (75 m/min faster)

Gary's distance:

200T (we really do not know the time or actual distance)

Faizal's distance:

125T

Is 125T 5/8 of 200T?

(5/8) 200T = 5(25)T = 125T (check)