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?
4 answers
it is for grade 7 level
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
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
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
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!!!!