Albert raced 4 times as fast as Bernhard. Albert raced 48 miles in 3 hours less than it took Bernhard to race 30 miles. How fast did each of them race? What were the times of each other?

Answer 1

To solve this question, we can use a system of equations.

If we say that A is the speed with which Albert raced and B is the speed with which Bernhard raced, we find that A = 4B because Albert raced 4 times faster than Bernhard. If A and B were measured in miles per hour, then we could say that B*h = 30 because the speed multiplied by time (h in hours) will give us the distance he traveled. Similarly, we say that A*(h-3) = 48 because Albert traveled 48 miles in 3 hours fewer than Bernhard.

This gives us three equations:

1. A=4B
2. Bh=30
3. A(h-3)=48

Now we can solve for our unknown values:

First, plug-in 4B from our first equation into A in our third equation: 4B(h-3)=48

Next, distribute the 4B: 4Bh - 12B = 48

Next, plug-in the value of Bh: 4(30) - 12B = 48

Next, simplify and solve for B: 120 - 12B = 48 -> 120 - 48 = 12B -> 72 = 12B -> B = 6

Next, find A using the first equation and plugging in B: A=4(6)=24 -> A=24

Finally, find h using the second equation and plugging in B: (6)h = 30 -> h = 5

Albert raced at 24 mph and Bernhard raced at 6 mph. Bernhard raced for 5 hours and Albert raced at 3 hours fewer than that, so Albert raced for 2 hours.

Let me know if you have any questions!

Answer 2

A=4B where A = Albert's speed, and B = Bernard's speed

d=rt

distance = speed x time

48=A(tb-3) where tb is Bernard's time to complete 30 miles: 30=Btb, tb= 30/B

48=4B(30/B-3)

12 = B(30/B -3)

12 =30 -3B

3B= 30-12 = 18

B = 18/3 = 6 mph

A = 4(6) = 24 mph