Elena bicycles 5km/h faster than Dennis. In the same time it takes Dennis to bicycle 57 km, Elena can bicycle 72 km. How fast does each bicyclist travel.
There was another variation I looked at of this, but the person who answered did not answer well enough where I was able to figure it out. So if someone can try again and dummy it down a bit for me to undestand I'd appreciate it. Thanks.
let Dennis' rate be x km/h
then Elena's rate is x+5 km/h
remember time = distance/rate
time for Dennis' trip = 57/x
time for Denise's trip = 72/(x+5)
But we are told the two times are the same
so
57/x = 72/(x+5)
cross-multiply
72x = 57x + 285
15x = 285
x = 19
so Dennis goes 19 km/h and Elena goes 24 km/h
To solve this problem, let's assign variables to the speeds of Dennis and Elena. Let's say Dennis's speed is "x" km/h, which means Elena's speed will be "x + 5" km/h because she is biking 5 km/h faster.
Next, we need to find the time it takes for both Dennis and Elena to cover their respective distances. Dennis bikes 57 km, and Elena bikes 72 km. Since time equals distance divided by speed, we can write two equations:
For Dennis: Time = Distance / Speed
For Elena: Time = Distance / Speed
Substituting the distances and speeds:
For Dennis: Time = 57 / x
For Elena: Time = 72 / (x + 5)
Since both Dennis and Elena take the same time, we can set their time equations equal to each other:
57 / x = 72 / (x + 5)
Now we can solve for x.
To simplify the equation, we can cross-multiply:
57(x + 5) = 72x
Distributing:
57x + 285 = 72x
Next, subtract 57x from both sides of the equation:
285 = 72x - 57x
285 = 15x
Now, divide both sides of the equation by 15 to solve for x:
285 / 15 = x
x = 19
So, Dennis bikes at a speed of 19 km/h. To find Elena's speed, we add 5 km/h to Dennis's speed:
Elena's speed = 19 + 5 = 24 km/h
Therefore, Dennis travels at 19 km/h and Elena travels at 24 km/h.