A car travels 315 miles in the same amount of time that a bus travels 245 miles. The rate of the car is 10 mph faster than the bus. Find the rate of the bus
since times are equal, and time = distance/speed
315/(b+10) = 245/b
b = 35
bus = 35 mph
car = 45 mph
check:
315/45 = 7
245/35 = 7
Let's denote the rate of the bus as 'r' mph.
Given that the car travels 315 miles and the bus travels 245 miles in the same amount of time, and the rate of the car is 10 mph faster than the bus, we can set up the following equation:
315 / (r + 10) = 245 / r
To solve for 'r', we can cross-multiply:
315r = 245(r + 10)
Expanding the equation:
315r = 245r + 2450
Simplifying the equation:
315r - 245r = 2450
70r = 2450
Dividing both sides of the equation by 70:
r = 35
Therefore, the rate of the bus is 35 mph.
To find the rate of the bus, let's assume that the rate of the bus is x mph.
Given that the car travels 315 miles in the same amount of time as the bus travels 245 miles, we can set up the following equation:
Time taken by the car = Time taken by the bus
Distance/Rate of the car = Distance/Rate of the bus
315/(Rate of the bus + 10) = 245/Rate of the bus
To solve this equation, cross-multiply:
315 * Rate of the bus = 245 * (Rate of the bus + 10)
315 * Rate of the bus = 245 * Rate of the bus + 245 * 10
315 * Rate of the bus - 245 * Rate of the bus = 245 * 10
(315 - 245) * Rate of the bus = 245 * 10
70 * Rate of the bus = 245 * 10
Divide both sides of the equation by 70:
Rate of the bus = (245 * 10) / 70
Rate of the bus = 24.5 * 10 / 7
Rate of the bus ≈ 35 mph
So, the rate of the bus is approximately 35 mph.