Question

places A and B are 160 km apart on same highway.If they travel in same direction they meet in 2 hours. If the travel in opposite directions they'll meet in 8 hours. Find the speed of each car​

Answer 1

correct question :-

places A and B are 160 are apart on same highway. one car starts from A and another starts from B at same time . if they travel in same direction they meet in 8 hrs . if they travel in opposite directions they'll meet in 2 hrs. find the speed of each car .

[this is the correct question because if both car traveling in same direction

(→ →), that means one car chase another, then they takes more time to meet . and while traveling in opposite directions (→←)they takes too less time]

we have :-

• if the both car traveling in same direction they meet in 8 hrs.
• if the both car traveling in opposite direction they meet in 2hrs.

To find :-

we have to find out the speed of both cars .

Solution based on :-

$\tt \: speed \: = \dfrac{distance}{time} \\ \\ \therefore \: \: \fbox{ \tt \: distance \: = \: speed × time}$

Solution :-

let speed of first car = x km/h

speed of second car = y km/h

• speed of both cars when both traveling in same direction = (x - y) km/h
• speed of both cars when both traveling in opposite direction = (x + y) km/h

ATQ

$\sf \: 8(x - y) = 160 \\ \sf \: x - y = 20 \: .............eq.(1) \\ \\ \sf \: 2(x + y) = 160 \\ \sf \: x + y = 80 \: ............eq.(1)$

add eq.(1) and eq.(2) , we obtain --

$\sf \: x - y = 20 \\ \sf \: x + y = 80 \\ \underline { \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \\ \sf \: 2x = 100 \\ \\ \sf \:x = \dfrac{100}{2} \\ \\ \bf \:x = 50 \:km/h$

substitute the value of x = 50 in eq.(2) we get --

$\sf \: x + y = 80 \\ \\ \sf \:50 + y = 80 \\ \\ \sf \:y = 80 - 50 \\ \\ \bf \:y = 30 \: km/h$

therefore

• the speed of first car = 50 km/h
• speed of second car = 30 km/h

.