Two cars travel the same distance. The first car travels at a rate of 37 mph and reaches its destination in t hours. The second car travels at a rate of 54 mph and reaches its destination in 3 hours earlier than the first car.
How long does it take for the first car to reach its destination?
Answer in units of hours.
Distance = rate * time
Let t = time for first car
37t = 54(t-3)
Solve for t.
37t = 54t-162
-17t = -162
t = 9.52941165
find an equation of variation where y varies directly as x,and y=7 when x= 3
Y varies directly as x,i.e x by y equal to 3 by 7
To find the time it takes for the first car to reach its destination, we can set up an equation based on its speed and the given information.
Let's say the time it takes for the first car to reach its destination is t hours. Since the distance traveled by both cars is the same, we can write:
Distance = Speed * Time
For the first car:
Distance = 37 mph * t hours
For the second car to reach its destination in 3 hours earlier than the first car, we need to subtract 3 from the time it takes for the first car to reach its destination. So, for the second car:
Distance = 54 mph * (t - 3) hours
Since both cars travel the same distance, we can set the two equations equal to each other:
37 mph * t hours = 54 mph * (t - 3) hours
Now, we can solve for t:
37t = 54(t - 3)
37t = 54t - 162
Collecting like terms, we get:
54t - 37t = 162
17t = 162
Dividing both sides by 17, we find:
t = 9
Therefore, it takes the first car 9 hours to reach its destination.