Question

Patrick travels from A to B at an average speed of 8km/h and then he travels from B to C at an average speed of 6 km/h.It is given that Patrick travels 26.4 km in 234 minutes for the whole journey.Find the distance that Patrick travels from A to B.​

Answer 1

12 km

Explanation:

So the situation is:

8 km/h for X hours

6 km/h for y hours

X * 8 + y * 6 = 26.4

and X + Y = 3.9 hours

Since 234/60 = 3.9 hours

You could write that X = 3.9 - Y

(3.9-Y) * 8 + y * 6 = 26.4

31.2 -8Y +6Y = 26.4

-2Y = -4.8

Y = 2.4 hours

X = 3.9-2.4 = 1.5 hours

So 1.5 * 8 = 12 km

Answer 2

AB = 12km

Explanation:

From the question we can get the following information,

The whole trip is 26.4 km and 3.9 hours (
`(234)/(60)`), and we can form the following two equations.

`x + y = 3.9` and
`(x*8km/h) + (y*6km/h) = 26.4km`

Where X is distance between A and B, and Y is distance between B and C. We can solve the first equation for X and plug X into the second equation.

`x = 3.9 - y` ........ and we can plug it into the the second equation and solve for y

`((3.9-y)*8)+(6y) = 26.4`

`(31.2-8y)+6y = 26.4`

`31.2-2y = 26.4`

`-2y = -4.8`

`y = 2.4`

Now we can plug in y to the first equation to solve for x

`x = 3.9-2.4`

`x = 1.5`

Finally, we can multiplay 8km/h by 1.5 hours to find the distance from A to B

`AB = 8km/h * 1.5h`

`AB = 12km`