Let Bernard's speed be B so he took 30/B hours to race 30 miles.

Three hours less than that is (30/B – 3) hours

Albert's speed A is given by A = 45/(30/B – 3)

But A = 3B

45 = 3B(30/B – 3) = 90 – 9B

Bernard's speed was 45/9 = 5 mph and he took 6 hours to go 30 miles

Albert's speed was 15 mph and he took 4 hours to go 45 miles

i) A = 3B

45/(3B) = 30/B - 3

15 = 30 - 3B

Bernard = 5 mph

Albert = 15 mph

ii) Albert = 3 hours

Bernard = 6 hours

Albert raced 3 times as fast as Bernard. In fact, Albert raced 45 miles in 3 hours less than it took Bernard to

race 30 miles. How fast did each of them race? What were the times of each racer?

A = 3B

T_Albert = T_Bernard - 3

45/A = 30/B - 3

Albert raced 3 times as fast as Bernard.

In fact, Albert raced 45 miles in 3 hours less than

it took Bernard to race 30 miles.

How fast did each of them race?

What were the times of each racer?

a = 3b

30/b - 45/a = 3

30/b - 45/3b = 3

10/b - 15/3b = 1

10/b = 1 + 15/3b

30 = 3b + 15

Solution:

a = 15, b = 5

a = 3b

45/a = 30/b - 3

45/(3b) = 30/b - 3

15 = 30 - 3b

b = 5

a = 15

Albert's speed was 15 mph and his time was 3 hours

Bernard's speed was 5 mph and his time was 6 hours