Mr. Higglebotham traveled 60 miles across the rainy English countryside at a constant rate of speed. If it had been sunny, he could have averaged 20 mph more and arrived at Broadmoor in 30 minutes less time. How fast was he driving?
I've gotten this far, but how do u solve for r? The answer is 40.
60 = rt
60 = (r + 20)(t - 1/2)
I've gotten this far, but how do u solve for r? The answer is 40.
60 = rt
60 = (r + 20)(t - 1/2)
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rt = 60
(r+20)(t-1/2) = 60
Solve the first equation for t, and substitute the result into the second equation to eliminate t from the system of equations:
t = 60/r
(r+20)(60/r - 1/2) = 60
Now, solve for r:
60r/r - r/2 + 20*60/r - 10 = 60
-r/2 + 1200/r - 10 = 0
r² -2400 + 20r = 0
r² + 20r - 2400 = 0
(r+60)(r-40) = 0
r = -60, 40
Discard the negative value since nowhere in the problem statement does it imply that Mr. Higglebotham was driving in reverse gear.
Mr. Higglebotham was driving 40 miles/hour.
(r+20)(t-1/2) = 60
Solve the first equation for t, and substitute the result into the second equation to eliminate t from the system of equations:
t = 60/r
(r+20)(60/r - 1/2) = 60
Now, solve for r:
60r/r - r/2 + 20*60/r - 10 = 60
-r/2 + 1200/r - 10 = 0
r² -2400 + 20r = 0
r² + 20r - 2400 = 0
(r+60)(r-40) = 0
r = -60, 40
Discard the negative value since nowhere in the problem statement does it imply that Mr. Higglebotham was driving in reverse gear.
Mr. Higglebotham was driving 40 miles/hour.
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Try substitution. Since you know that arranging the second equation in terms of r gives you
(60 - 20)/(t - 1/2)= r
substitute it for r in the first equation.
60 = 40t/(t - 1/2)
60(t - 1/2) = 40t
60t - 30 = 40t
20t = 30
t = 1.5
Substitute 1.5 for t in the first equation
60 = r(1.5)
40 = r
To check the answers, substitute 1.5 for t and 40 for r in the second equation
60 = (40 + 20)(1.5 - 0.5)
60 = 60 * 1
60 = 60
It works.
So he was going 40 mph for 60 miles, which would take 1 1/2 hours. If it were sunny, he would have been going 60 mph for 60 miles, which would take a 1/2 hour less, or one hour.
ANSWER
He was driving 40 mph ~ possibly in reverse because nowhere in the problem does it specify that he wasn't.
:)
(60 - 20)/(t - 1/2)= r
substitute it for r in the first equation.
60 = 40t/(t - 1/2)
60(t - 1/2) = 40t
60t - 30 = 40t
20t = 30
t = 1.5
Substitute 1.5 for t in the first equation
60 = r(1.5)
40 = r
To check the answers, substitute 1.5 for t and 40 for r in the second equation
60 = (40 + 20)(1.5 - 0.5)
60 = 60 * 1
60 = 60
It works.
So he was going 40 mph for 60 miles, which would take 1 1/2 hours. If it were sunny, he would have been going 60 mph for 60 miles, which would take a 1/2 hour less, or one hour.
ANSWER
He was driving 40 mph ~ possibly in reverse because nowhere in the problem does it specify that he wasn't.
:)
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you need to change the 1/2 to 30
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80 miles per hour