# Math Help - Linear word problems

1. ## Linear word problems

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

Formula: distance= speed * time

2. Originally Posted by delicate_tears

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

Formula: distance= speed * time
dont know if this is right for sure, let me know x-48 1/3 =30

3. Originally Posted by Leona_Marie
dont know if this is right for sure, let me know x-48 1/3 =30
what i meant was x-48 1/3 /2 = 30

4. Originally Posted by delicate_tears

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

Formula: distance= speed * time
Hi delicate_tears,

Let's see if I'm interpreting this problem correctly.

Let x = speed in km/h running

Let x + 30 = speed in km/hr cycling

48 minutes running = 48/60 = 4/5 hours

one-third as much again cycling seems like 48 + 1/3(48) = 64 minutes = 64/60 = 16/15 hours.

d = rate X time

d = 60

The distance traveled while running would be $\frac{4}{5}x$

The distance traveled while cycling would be $\frac{15}{16}(x+30)$

The two distances together would equal 60 km.

The linear equation would then be:

$\frac{4}{5}x+\frac{16}{15}(x+30)=60$

5. Hey Leona_Marie, thanks for replying first to my thread! Unfortunately I don't quite understand the equation you wrote as it contained too many slashes that I got mixed up.

Originally Posted by masters
Hi delicate_tears,

Let's see if I'm interpreting this problem correctly.

Let x = speed in km/h running

Let x + 30 = speed in km/hr cycling

48 minutes running = 48/60 = 4/5 hours

one-third as much again cycling seems like 48 + 1/3(48) = 64 minutes = 64/60 = 16/15 hours.

d = rate X time

d = 60

The distance traveled while running would be $\frac{4}{5}x$

The distance traveled while cycling would be $\frac{15}{16}(x+30)$

The two distances together would equal 60 km.

The linear equation would then be:

$\frac{4}{5}x+\frac{16}{15}(x+30)=60$
Hi masters, my interpretation of the problem is different to yours but your interpretation is actually the correct one.

Where the word problem says 'as third as much time again cycling' I wrote is as 1/3(48)= 16 minutes= 16/60 hr = 4/15 hr.

Thankyou so much