A man cycles to a village at 18 km/h and returns at 12 km/h. If he takes 6 1/4 hours for the double journey, how far does he ride altogether?

Question

This is Equations from Word Problems.

Answer 1

We basically use our clues here. It's logical to assume that:

The distance to and from the village are the same (Double journey)

So if we want to say the "distances" are the same in terms of the "speed"

We can say 18x = 12y or in other words, 18x is going trip, and 12y is the trip back.

X is the time going, Y is the time going home.

Also we know the TOTAL time is 6.25 hours, so we can say Time Going + Time Returning is 6.25

or in other words, x+y=6.25

Then we can use the substitution of "x" into the first equation to solve.

Equation 1: 18x = 12y
Equation 2: x+y=6.25, or if we re-arrange the equation x=6.25-y

18(6.25-y) = 12y

112.5-18y=12y

112.5=30y
y=3.75

So NOW we plug in 3.75 (y) into the 12y to figure out how long the distance is

12y * 3.75 is 45 kilometers (one way)

So TOTAL trip going is 45 kilometers, total trip coming home is 45 kilometers, total is 90 kilomeeters.

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Answer 2

18x = 12y                eq. 1

 

x + y = 6.25             eq. 2

 

x = 6.25 - y

 

substitute value of x to eq. 1

 

18(6.25 - y) = 12y

 

112.5 - 18y = 12y

 

112.5 = 12y + 18y

 

112.5 = 30y

 

y = 3.75

 

3.75 * 12 = 45

 

2 * 45 = 90 km