Need help with math word problem

Question

during a triathlon, sharon swims a quarter of the total route and cycles three fifths of the remaining route. she runs the rest of the route. if she runs 3600 meters, find the total distance of the triathlon route.

Answer 1

D/4 + 3D/5 +3600 = D

 

Let's start by getting a similar denominator so we can find out how much of the triathlon is ran. 20 is the lowest common denominator for 4 & 5:

 

5D/20 + 12D/20 + 3600

 

20 - 5 - 12 = 3

 

so 3D/20 is ran.

 

3D/20 = 3600

Now we isolate for D:

 

3D = 72000

D = 24000 meters

 

Now let's put that into our original equation to make sure we have it right:

 

D/4 + 3D/5 +3600 = D

24000/4 + 3 * 24000 / 5 + 3600 = 24000

6000 + 72000 / 5 + 3600 = 24000

6000 + 14400 + 3600 = 24000

20400 + 3600 = 24000

24000 = 24000