To travel 88 miles, it takes Sue, riding a moped, 4 hours less time than it takes Doreen to travel 72 miles riding a bicycle. Sue travels 13 miles per hour faster than Doreen. Find the times and rates of both girls.
Doreen _ mph for _ hr
Sue _ mph for _ hr
Vs*Ts = 88
(Vs-13)(Ts+4) = 72
22*4 = 88
9*8 = 72
To find the times and rates of both girls, let's first find their individual speeds.
Let's assume Doreen's speed is x mph. Since Sue travels 13 miles per hour faster than Doreen, Sue's speed will be x + 13 mph.
Now, to find the times taken by both girls, we can use the formula:
Time = Distance / Speed
For Doreen, riding a bicycle for 72 miles at a speed of x mph, her time can be calculated as:
Time taken by Doreen = 72 miles / x mph
And for Sue, riding a moped for 88 miles at a speed of (x + 13) mph, her time can be calculated as:
Time taken by Sue = 88 miles / (x + 13) mph
Given that Sue takes 4 hours less time than Doreen, we can set up the equation:
Time taken by Sue = Time taken by Doreen - 4 hours
88 miles / (x + 13) mph = 72 miles / x mph - 4 hours
To solve this equation, we can cross multiply and simplify:
88x = 72(x + 13) - 4x
88x = 72x + 936 - 4x
88x - 72x = 932
16x = 932
x = 932 / 16
x = 58
Now, substituting the value of x back into our equations, we can find the individual speeds and times:
Doreen's speed = x mph = 58 mph
Sue's speed = x + 13 mph = 58 + 13 = 71 mph
Time taken by Doreen = 72 miles / x mph = 72 miles / 58 mph ≈ 1.24 hours (approximately)
Time taken by Sue = 88 miles / (x + 13) mph = 88 miles / 71 mph ≈ 1.24 hours (approximately)
Therefore,
Doreen's speed is 58 mph, and she takes approximately 1.24 hours to cover 72 miles.
Sue's speed is 71 mph, and she also takes approximately 1.24 hours to cover 88 miles.