# Please help solve this advanced general mathematics worded question involving linear equations.A biathlon event involves running and cycling. Kim can cycle 30km/h faster than she can run. If Kim...

Please help solve this advanced general mathematics worded question involving linear equations.

A biathlon event 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 60km, how fast can she run?

working out shown please.

### 2 Answers | Add Yours

Kim can cycle 30 km/h faster than she can run. If the speed at which she can run is X, the speed at which she can cycle is X + 30.

She spends 48 minutes running and 48/3 = 16 minutes cycling. The total distance covered is 60 km.

Distance = speed*time

=> 60 = X*(48/60) + (X + 30)*(16/60)

=> 3600 = 48X + 16X + 480

=> 60X = 3120

=> X = 52

**The speed at which Kim can run is 52 km/h.**

Thank you for that 'justaguide', but your answer does not match my book's. The mistake you made was in the addition of 16 and 48 minutes, which equals 64 minutes not 60.