Elena bicycles 4 km/h faster than Robert. In the same time it takes Robert to bicycle 27km/h, Elena can bicycle 39 km. How fast does each bicycle travel?
It would help if you proofread your questions before you posted them (27km/h).
Robert's speed = x and Elena's = x + 4
time = distance/rate
27/x = 39/(x+4)
Solve for x, then x+4.
To find the speeds of Robert and Elena, let's set up a system of equations.
Let's assume Robert's speed is x km/h. Since Elena bicycles 4 km/h faster, Elena's speed will be (x + 4) km/h.
Since they both take the same time to travel their respective distances, we can set up the equation:
Time taken by Robert = Time taken by Elena
Distance / Speed = Distance / Speed
27 / x = 39 / (x + 4)
To solve the equation, we can cross-multiply:
27(x + 4) = 39x
27x + 108 = 39x
Now, let's simplify the equation:
108 = 39x - 27x
108 = 12x
To solve for x, divide both sides by 12:
9 = x
Therefore, Robert's speed is 9 km/h.
Now, to find Elena's speed, substitute the value of x back into the equation:
Elena's speed = x + 4 = 9 + 4 = 13 km/h.
So, Robert's speed is 9 km/h and Elena's speed is 13 km/h.