Question

truck travelled from Town A to Town B. A van travelled from Town B to Town A at the same time . They met 10 km from the middle of the journey. Find the distance between Town A and Town B if the truck and the van travelled at 85 km / h and 60 km / h respectively .​

Answer 1

58 miles

Explanation:

One truck second truck

rate 85 60

time t t

Distance d + 10 d -10

d + 10 = 85t d - 10 = 60t

d = 85= -10 d = 60t +10

Set the two equations equal to each other and solve

85t -10 = 60t + 10 Subtract 60t from each side

25t - 10 = 10 Add 10 to each side

25 t = 20 Divide both sides by 25

t =
`(4)/(5)`

Each were driving 4/5 of an hour. Plug into the one of the equaions

d + 10 = 85t

d + 10 = 85(
`(4)/(5)`)

d +10 = 68 Subtract 10 from both sides

d = 58

Answer 2

Explanation:

Givens

Truck = 85 km/hr

Van = 65 km/hr

t is the time they meet

Note

Truck A is travelling faster, so the place where they meet is closest to Town B.

Solution

Let the distance travelled by the truck be

d/2 + 10

Let the distance travelled by the van be

-d/2 + 10

Let t be the time they meet

85* (d/2 + 10) /t = -60*(d/2 + 10)/t multiply both sides by t

85*(d/2 + 10)*t/t = -60*(d/2 + 10)*t/t Combine

85*(d/2 + 10) = -60(d/2 + 10) Remove the brackets.

42.5 d + 850 = -30d - 600 Add 30 d to both sides

72.5d+ 850 = - 600 Subtract 850 from both sides.

72.5d = - 600 - 850 Combine

72.5d = -1450 Divide by 72.5

d = -1450 / 72.5

d = -20

The minus means that you are looking at it from the van's point of view.