What are the average speeds of the car from Lewiston and the car from Vernonvile?
Mathematics

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Lewiston and Vernonville are 128 miles apart. A car leaves Lewiston traveling towards Vernonville, and another car leaves Vernonville at the same time, traveling towards Lewiston. The car leaving Lewiston averages 10 mph more than the other, and they meet after 1 hour and 36 minutes. What are the average speeds of the cars?
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Distance = 128 miles
Let speed of the car leaving Vernonville be x mph
So the speed of the car that leaves Lewiston is (x + 10) mph
So their relative speed is x + x + 10 = (2x + 10); since they are travelling in opposite direction.
Time taken to meet = Distance / Relative Speed
T = 1 hr 36 min = 1.6 hr
1.6 = 128/(2x + 10)
1.6(2x + 10) = 128
3.2x + 16 =128
3.2x =112
x = 35 mph
So the average speeds for the cars are 35 mp and 45 mph.
if a plane can travel 470 mph with the wind and 390 mph against the wind, find the speed of the plan in still air. What is the speed of the plane in still air?
let x be the speed of the plane in still air
and z be the speed of the wind
Speed of plane with wind = x + z
Speed of plane against wind= x  z
So we have the following system of equations:
{ x + z = 470. . . . .1
{ x  z = 390. . . . 2
Adding both we get 2x = 860
x = 430 mph.
Therefore, the speed of the plane in still air is 430 mph.
Awesome help! Thank you so much
A baseball team has home games on Thursday and Sunday. The games together earn $4051.00 for the team. Thursday's game generates $61.00 less than Sunday's game. How much money was taken in at each game\
Let the amount generated by the Sunday game be x
So the Thursday game will generate x  61, i.e. Thursday's game generates $61.00 less than Sunday's game
Total =$ 4051.00
so x + (x61) = 4051
2x61= 4052
2x= 4113
x = 2056.5
So the Sunday game generated $ 2056.50 while the Thursday game generated $(2056.50  61) which is $1995.50
Thank you so much! xo
It would cost $80.50 to buy three tickets in Japan plus two tickets in Switzerland. Three tickets in Switzerland plus two tickets in Japan would cost $79.90. How much does an average movie ticket cost in Japan and how much in Switzerland." Thank you
let the cost of one ticket bought in japan be $ j and that bought in Switzerland be $ s
So
3j + 2s = 80.50 since It would cost $80.50 to buy three tickets in Japan plus two tickets in Switzerland
3s + 2j = 79.90 since three tickets in Switzerland plus two tickets in Japan would cost $79.90.
Now you have simultaneous equation which can be solved by substitution or by elimination.
Now rearrange
3j + 2s = 80.50
2j + 3s = 79.50
I will solve via elimination
2{ 3j + 2s = 80.50
3{2j + 3s = 79.50
6j + 4s = 161
6j + 9s = 238.5
Subtract the second equation from the first
 5s = 77.5
s = 15.5
Now find j by substituting s in any of the above equation:
3j + 2s = 80.50
3j + (2 x 15.5) = 80.50
3j + 31= 80.50
3j = 49.5
j = 16.5
So the average cost for a movie ticket in Japan is $ 16.50 and in Switzerland is $ 15.50
Thank you!
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