A car travelling at an average speed of 55kph leaves Town A for Town B a distance of 120 kilometres. At the same time, another car, travelling on the same highway at an average speed of 45kph, leaves Town B for Town A. In how many leaves will they meet? How far from Town A will they meet?
I will assume you have learned how to use variables.
Let the distance from A to the meeting point be x km
then the distance from B to the meeting point is 120-x km
time from point A = x/55
time from point B = (120-x)/45
but those two times must be equal, they both left at the same time.
x/55 = (120-x)/45
cross-multiply
45x = 6600 - 55x
100x = 6600
x = 66
They will meet 66 km from town A
the time will be x/55 or 66/55 = 6/5 hrs
which is 1 hour and 12 minutes
(notice I would get the same time if I had used
(120-x)/45
= (120-66)/45
= 54/45
= 6/5
it is for grade 7 level
V = Velocity
L = Length
t = Time
LA = Distance between meeting point and town A
LB = Distance between meeting point and town B
L = LA + LB = 120 km
LA + LB = 120 Subtract LA to both sides
LA + LB - LA = 120 - LA
LB = 120 - LA
VA = Velocity of a car which travelling town A for town B
VA = LA / t = 55
55 = LA / t Multiply both sides by t
55 t = LA Divide both sides by 55
t = LA / 55
VB = Velocity of a car which travelling town B for town A
VB = LB / t = 45
45 = LB / t Multiply both sides by t
45 t = LB Divide bot sides by 45
t = LB / 45
t = t
LA / 55 = LB / 45
LA / 55 = ( 120 - LA ) / 45 Multiply both sides by 55
LA = 55 * ( 120 - LA ) / 45 Multiply both sides by 45
45 * LA = 55 * ( 120 - LA )
45 LA = 55 * 120 - 55 * LA
45 LA = 6,600 - 55 LA Add 55 LA to both sidas
45 LA + 55 LA = 6,600 - 55 LA + 55 LA
100 LA = 6,600 Divide both sides by 100
LA = 6,600 / 100
LA = 66 km
LB = 120 - 66 = 54 km
t = LA / 55 = 66 / 55 = 1.2 h = 1 h 12 min
OR
t = LB / 45 = 54 / 45 = 1.2 h = 1 h 12 min
Thank you very much for your help!!!!
To find out how many hours it will take for the two cars to meet and the distance from Town A where they will meet, we can use the concept of relative speed.
Relative speed is the combined speed of two objects moving in the same direction or opposite directions. When two objects move towards each other, we can add their speeds to find the relative speed. When they move in the same direction, we subtract the speed of one object from the other to get the relative speed.
Let's break down the problem step by step:
Step 1: Calculate the relative speed.
Since the two cars are moving towards each other, we need to calculate the sum of their speeds. The combined speed is 55 kph (car A) + 45 kph (car B) = 100 kph (relative speed).
Step 2: Calculate the time it will take for the two cars to meet.
To find the time it takes for the two cars to meet, we divide the distance between them by the relative speed.
120 kilometers (distance between the towns) / 100 kph (relative speed) = 1.2 hours
So, the two cars will meet after 1.2 hours.
Step 3: Calculate the distance from Town A where they will meet.
To find the distance from Town A where the cars will meet, we can multiply the speed of car A by the time it takes for them to meet.
Speed of car A = 55 kph
Time taken = 1.2 hours
Distance = Speed * Time
Distance = 55 kph * 1.2 hours = 66 kilometers
Therefore, the two cars will meet after 1.2 hours, and they will meet 66 kilometers away from Town A.