Final answer:
The car's speed is 98/4.67 mph and the bus's speed is 107/4.67 mph.
Step-by-step explanation:
Let's assume the speed of the car is x miles per hour. According to the given information, the bus averages 9 miles per hour faster than the car, so the speed of the bus is x + 9 miles per hour.
We can use the formula, speed = distance/time, to solve this problem. In the same time it takes the car to travel 98 miles, the bus travels 140 miles. So we have the equations:
x = 98/(time taken by the car)
x + 9 = 140/(time taken by the car)
To find the speed of each, we can solve these equations simultaneously.
Let's assume the time taken by the car is t hours. So, the time taken by the bus is also t hours.
Now we can solve the equations:
- x = 98/t
- x + 9 = 140/t
By substituting the value of x from equation 1 into equation 2, we get:
98/t + 9 = 140/t
Multiplying both sides of the equation by t, we get:
98 + 9t = 140
Subtracting 98 from both sides of the equation, we get:
9t = 42
Dividing both sides of the equation by 9, we get:
t = 42/9
Simplifying, we get:
t = 4.67 hours
Therefore, the speed of the car is x = 98/4.67 miles per hour and the speed of the bus is x + 9 = 107/4.67 miles per hour.