Keiko bicycles 8 km/h faster than robert. in the same time it takes Robert to bicycle 27 km, Keiko can bicycle 51 km. how fast does each bicyclist travel?

Question

I need help with this math problem please!

Answer 1

 

 

Let

x = Robert's speed

 

 x + 8 = Keiko's speed

 

t = the time that both Robert and Keiko travel.

 

We use the standard formula

speed x time - distance.

Then,

xt = 27    This is the distance Robert travels

And

(x + 8)t = 51 This is the distance that Keiko travels.

 

We can solve for t in both formulas

 

t = 27/x

and

t = 51/(x + 8)

 

Now, by the transitive property,

 

27/x = 51/(x + 8)

27(x + 8) = 51x

27x + 216 = 51x

216 = 24x

x = 9 km/h This is Robert's speed

x + 8 = 17 km/h  This is Keiko's speed