# Thread: Algebra help

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?

Here is my answer:

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?

2. I am not sure that this will help you but I did this a different way and got your answers.

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?

Grandad

4. Originally Posted by Grandad
Hello 22upon7Can you see where you went wrong?

Grandad
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.

Grandad

6. Thanks for that!