You can travel 40 miles on a motorcycle in the same time that it takes to travel 15 miles on a bicycle. If your motorcycle's rate is 20 miles per hour faster than your bicycle's rate, find the speed of the motorcycle and bicycle.
motorcycle = 32mph
bicycle = 12 mph
Are these correct?
D=RT
40=(20+B)T
15=BT (15/T)=b
40=(20+(15/T))T
40/t=20+15/t
25/t=20
25=20t
t= one and one fourth
B=(15/(5/4))=12
12+20=32
B=12
M=32
You are correct
Thanks.
To solve this problem, we can use the formula Time = Distance / Speed.
Let's assume the speed of the bicycle is x mph. Since the motorcycle is 20 mph faster than the bicycle, the speed of the motorcycle would be x + 20 mph.
Now, using the formula Time = Distance / Speed, we can set up two equations:
For the motorcycle: Time = 40 miles / (x + 20 mph)
For the bicycle: Time = 15 miles / x mph
According to the given information, the time it takes to travel 40 miles on the motorcycle and 15 miles on the bicycle is the same. Therefore, we can set up the equation:
40 miles / (x + 20 mph) = 15 miles / x mph
To solve this equation, we can cross-multiply: (40 miles) * x = (15 miles) * (x + 20 mph)
40x = 15x + 300
Simplifying the equation, we get:
25x = 300
Dividing both sides by 25, we find:
x = 12 mph
So, the speed of the bicycle is 12 mph.
The speed of the motorcycle would be x + 20 mph, which is 12 mph + 20 mph = 32 mph.
Therefore, your answers are correct! The speed of the motorcycle would be 32 mph, and the speed of the bicycle would be 12 mph.