Answer:
Brian's speed = 70 mph
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Work Shown:
B = brian's speed
J = jake's speed
both speeds are in miles per hour (mph)
We're told that "Jake's speed was 15 mph slower than Brian's speed", so
Jake's speed = (brian's speed) - 15
J = B - 15
We'll use this equation later, so set it aside for now.
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Now move onto the distance rate time equation d = r*t. Basically you multiply the rate (or speed) by the time to get the distance traveled.
For Brian, he travels at a speed of B mph and does so for 4 hours. His equation is d = r*t ---> d = B*4 ----> d = 4B
For Jake, its the same story but we use J instead of B. So we have d = 4J
The two distance expressions are 4B and 4J which add to 4B+4J = 4(B+J)
This is then set equal to 500 to get the equation 4(B+J) = 500
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Let's go back to J = B-15 and plug this into the equation we just got above
4(B+J) = 500
4(B+B-15) = 500 .... J replaced with B-15
4(2B-15) = 500
2B-15 = 500/4 ... divide both sides by 4
2B - 15 = 125
2B = 125+15 ... add 15 to both sides
2B = 140
B = 140/2 ... divide both sides by 2
B = 70
Brian's speed is 70 mph
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Extra Info:
If you're curious about Jake's speed, then plug B = 70 into J = B-15 to get
J = B-15
J = 70 - 15
J = 55
So Jake is going 55 mph