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

Mathematics
Tutor: None Selected Time limit: 1 Day

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?

Jun 7th, 2015

Thank you for the opportunity to help you with your question!

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.



Please let me know if you need any clarification. I'm always happy to answer your questions.
Jun 7th, 2015

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.





Jun 7th, 2015

Awesome help!  Thank you so much 

Jun 7th, 2015

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 + (x-61) = 4051

2x-61= 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

Jun 7th, 2015

Thank you so much! xo

Jun 7th, 2015

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


Jun 7th, 2015

Thank you!

Jun 7th, 2015

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