Question

17. Places A and B are 80 km apart from each other on a highway. A car starts from A and
another from B at the same time. If they move in same direction they meet in 8 hrs and if
they move in opposite directions they meet in 1 hr 20 minutes. Find speeds of the cars.​

Answer 1

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Answer 2

Answer-

Speed of car A = 35 km/hr and B = 25 km/hr

$\rule{100}2$

Step-by-step explanation-

Let the speed of car which starts from A be x km/hr and B be y km/hr.

Case 1)

Places A and B are 80 km apart from each other on a highway. A car starts from A and another from B at the same time. If l they move in same direction they meet in 8 hrs.

Time = 8 hrs and distance = 80 km

Both cars are moving in same direction. So, speed = (x - y) km/hr

Time = Distance/Speed

⇒ 8 = 80/(x - y)

⇒ x - y = 80/8

⇒ x - y = 10

⇒ x = 10 + y

Case 2)

If both cars move in opposite direction then they meet in 1 hr 20 min.

Now, speed = (x + y) km/hr

Time = 1 hr 20 min = (1 + 20/60) = 4/3 hrs.

Distance = 80 km

⇒ 4/3 = 80/(x + y)

⇒ x + y = (80 × 3)/4

⇒ x + y = 60

From above we can write it like,

⇒ 10 + y + y = 60

⇒ 2y = 50

⇒ y = 25 km/hr

Substitute value of y in x

⇒ x = 10 + 25

⇒ x = 35 km/hr