doubt for word problem experts

Question

A man performs 3/5 of the total journey by rail 17/20 by bus and remaining 6.5 km on foot his total journey is ?

i know the answer and how to solve but i have doubt
please understand my doubt

a man performs 3/5 of the total journey by rail 17/20 by bus
now when we are assuming x as total journey
so we did as question directs to do

 

1  now 3/5 of total journey in math we do 3/5x, 3/5x he traveled by rail

 

2   now 17/20 by bus so conclusion is 17/20 he traveled by bus. they not state that 17/20 of total journey by bus then our in conclusion will be 17x/20

 

how i get to know that when should i take variable for multiply with fraction and when shouldn't

Answer 1

Hi Amey, the question is misleading. If x is the total distance traveled and he traveled 3/5 of the distance by rail, that leaves only 2/5 of the remaining distance traveled by bus and includes the 6.5 kilometers he walked.

 

The equation looks like this:

 

Total distance traveled - distance traveled by rail - distance traveled by bus - distance walked = 0

 

x (total distance) - 3/5 * x (distance by rail) - 17/20 * 2/5 * x (distance by bus) - 6.5 (distance walked) = 0

 

This becomes:

 

x - 3/5 * x - 34/100 * x - 6.5 = 0

 

x - 60/100 * x - 34/100 * x = 6.5

 

x - 94/100 * x = 6.5

 

6/100 * x = 6.5

 

Multiply both sides by 100

 

6x = 650

 

Divide both sides by 6

 

x = 108.33 

 

Total distance traveled is 108.33 kilometers.

 

Check

 

3/5 or .6 times 108.33 ≈ 65 kilometers traveled by rail.

 

That leaves 43.33 kilometers traveled by bus and on foot.

 

17/20 or .85 times 43.33 = 36.85 kilometers traveled by bus.

 

That leaves 6.5 kilometers traveled on foot.

 

65 (by rail) + 36.85 (by bus) + 6.5 (on foot) = 108.33

 

Questions?