1. ## Algebra help

I have been trying to work this sum out for some time now, But I cant get a proper answer.

Heres the sum, my answer can be found below

A biathalon even involves running and cycling. Kim can cycle 30km/h faster than she can run. If Kim spends 48 minutes running and a third as much time again cycling in an event that covers a total distance of 60 km, how fast can she run?

Running speed = $x km/h$
cycling speed = $x + 30 km/h$

$\frac{48}{60} \times x+\frac{16}{60} \times (x+30)=60$

$x=48.75$

This is wrong because the book says the answer is 15 km/h

What am I doing wrong here?

cycle: rate = (x+30)km/hr; t = .26 hours
run: rate = x km/hr; t = .8 hours

using d = rt

d = .26(x + 30)
60 - d = .8x

60 - .26x - 7.8 = .8x
52.2 = 1.06x
x = 49.24...its about the same with rounding error. I've looked and I've looked but I can't see the error. Sorry.

3. ## Algebra problem

Hello 22upon7
Originally Posted by 22upon7
If Kim spends 48 minutes running and a third as much time again cycling ...
Can you see where you went wrong?

Hello 22upon7Can you see where you went wrong?

No unfortunately I don't, Doesn't it mean that she ran for 48 minutes and cycled for 16 minutes?

5. ## Algebra problem

Hello 22upon7
Originally Posted by 22upon7
If Kim spends 48 minutes running and a third as much time again cycling ...
The key is in the word 'again' which means you take the original time plus a third as much again. So she spends 48 + 16 = 64 minutes cycling. Sorry, I thought you would have known that, or I would have explained more clearly the first time.