I NEED HELP PLEASE!!!!!!!!!!
Elena bicycles 7 km/h faster than Dennis. In the same time it takes Dennis to bicycle 60km, Elena can bicycle 81km. How fast does each bicyclist travel.
Dennis travel_____ km/h
Elena travel ______ km/h
let Dennis' rate be x km/h
let Elena's rate be x+7 km/h
time taken by Dennis = 60/x
time taken by Elena = 81/(x+7)
but their times are equal, so
60/x = 81/(x+7)
cross-multiply and solve for x
then find x+7 for Elena's rate
To find the speeds at which Dennis and Elena travel, we can set up a system of equations based on the given information.
Let's assume that Dennis travels at a speed of x km/h. Since Elena bicycles 7 km/h faster, her speed can be represented as (x + 7) km/h.
Now, we know that the time it takes Dennis to bicycle 60 km is the same as the time it takes Elena to bicycle 81 km. This means that their time is constant.
We can use the formula: time = distance / speed.
For Dennis, the time is 60 km divided by his speed (x km/h), so:
60 / x = time
For Elena, the time is 81 km divided by her speed (x + 7 km/h), so:
81 / (x + 7) = time
Since the times are equal, we can set up the following equation:
60 / x = 81 / (x + 7)
To solve this equation, we can cross-multiply:
60(x + 7) = 81x
Expanding the equation:
60x + 420 = 81x
Moving all the terms involving x to one side of the equation:
81x - 60x = 420
21x = 420
Dividing both sides of the equation by 21:
x = 420 / 21
Simplifying:
x = 20
So, Dennis travels at a speed of 20 km/h.
To find Elena's speed, we can substitute this value back into one of the earlier equations:
Elena's speed = Dennis' speed + 7
Elena's speed = 20 + 7
Elena's speed = 27 km/h
Therefore, Dennis travels at 20 km/h, and Elena travels at 27 km/h.