Your family decides to visit your grandparents that live in ohio. You drive at an average rate of 55 mph when driving in Indiana and 65 mph when driving in Ohio. The entire trip of 295 miles takes 5 hours. How long does it take to reach the Indiana-Ohio border?
How many miles did you drive before you reached the border?
From which direction did you come?
It starts in Indiana. It doesn't say if it is north, south, east, or west. Indiana is west of Ohio, though.
If it helps, we are working with linear combinations (elimination) and substitution. We are supposed to use whatever method works best.
Is this just an odd question? I've been able to solve every problem except for this one.
It doesn't make any sense to me.
You know takes to drive 5 hours to go 295 miles. But the problem gives no indication where that 295 miles is.
Please ask your teacher about this one.
Alright. Thank you! :)
To determine how long it takes to reach the Indiana-Ohio border, we need to find the distance traveled in Indiana. We can then calculate the time it takes by dividing the distance by the average speed in Indiana.
Let's assume the distance from the starting point to the Indiana-Ohio border is D miles.
We know that the total trip is 295 miles, and we are given the average speed in Indiana as 55 mph. So, the distance traveled in Ohio can be found by subtracting the distance traveled in Indiana from the total trip distance:
Distance in Ohio = Total distance - Distance in Indiana
Distance in Ohio = 295 miles - D miles
Distance in Ohio = (295 - D) miles
The time it takes to travel in Indiana can be calculated by dividing the distance in Indiana by the average speed in Indiana:
Time in Indiana = Distance in Indiana / Average speed in Indiana
Time in Indiana = D miles / 55 mph
Time in Indiana = D/55 hrs
Time in Indiana = (D/55) hours
We also know that the average speed in Ohio is 65 mph. The distance traveled in Ohio can be divided by the average speed to calculate the time taken in Ohio:
Time in Ohio = Distance in Ohio / Average speed in Ohio
Time in Ohio = (295 - D) miles / 65 mph
Time in Ohio = (295 - D)/65 hrs
Since the total trip time is given as 5 hours, the sum of the time taken in Indiana and Ohio should equal 5:
Time in Indiana + Time in Ohio = 5
Plugging in the calculated time values:
(D/55) + (295 - D)/65 = 5
Now we can solve this equation to find the value of D, the distance traveled in Indiana.
Cross-multiplying and simplifying:
65D + 55(295 - D) = 5 * 55 * 65
65D + 16225 - 55D = 17875
10D = 16450
D = 1645
So, the distance traveled in Indiana is 1645 miles. To find the time taken to reach the Indiana-Ohio border, we can substitute this value into the equation for time in Indiana:
Time in Indiana = D/55
Time in Indiana = 1645/55
Time in Indiana ≈ 29.91 hours
Therefore, it takes approximately 29.91 hours to reach the Indiana-Ohio border.