Question 74258: can you help me in solving the problem...
ariana took 2 h longer to drive 360 mi on the first day of a trip than she took to drive 270 mi on the second day. if her speed was the same on both days, what was the driving time each day?
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! We're going to use the equation that says Distance (D) is equal to the Rate (R) times the Time (T)
or in equation form:
.
D = R*T
.
On the second day she drove 270 miles in the time T. In equation form this is:
.
270 = R*T
.
Solve this equation for R by dividing both sides by T to get R = 270/T
.
On the first day she drove 360 miles in the time T+2. In equation form this is:
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360 = R*(T+2)
.
Solve this equation for R by dividing both sides by (T+2) to get R = 360/(T+2)
.
The problem then says the R is the same on both days. Since it equals 360/(T+2) on the
first day and 270/T on the second day we can set these two equal to get:
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360/(T+2) = 270/T
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Multiply both sides by (T+2) to get rid of the denominator on the left side and you get:
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360 = 270*(T+2)/T
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Then multiply both sides by T to get rid of the denominator on the right side. The equation becomes:
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360T = 270*(T+2)
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Multiply out the right side and the equation further becomes:
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360T = 270T + 540
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Next get rid of the 270T on the right side by subtracting 270 from both sides of the equation:
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90T = 540
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Now you can solve for T by dividing both sides of the equation by 90 and the result is:
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T = 540/90 = 6
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So the time (T) which is the driving time on the second day is 6 hours. That means that
on the first day she drove 2 additional hours for a total driving time on the first day
of 8 hours.
.
Another and quicker way you could have done this problem is to say that that on the first
day she spent 2 more hours on the road and she drove 90 more miles (360 miles on that day
and 270 miles on the second day). So in those 2 hours she averaged 45 miles per hour to cover
those 90 miles in 2 hours. So at 45 miles per hour it would take 8 hours to cover the
360 miles. On the second day she still drove at 45 mph and to cover 270 miles divide 270 by 45
and find that it took 6 hours.
.
Hope these two approaches to solving the problem give you some insight into the relationship
among distance, rate, and time.
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