A high-speed train makes a 360 mile nonstop run between two major cities in 712 hours. The train travels 80 mph in the country, but safety regulations require that it travel only 20 mph when passing through smaller, intermediate cities. How many hours are spent traveling through the smaller cities?
712 hrs ??? , that would be a whole month !
I will assume you meant 7 1/2 hrs or 7.5 hrs
let the distance in the country be x miles
then the distance through towns is 360-x miles
x/80 + (360-x)/20 = 7.5
multiply by 80 , the LCD
x + 4(360-x) = 600
x + 1440 - 4x = 600
-3x = -840
x = 280
so 280 miles through country and 80 miles through towns
time in towns = 80/20= 4 hrs
Thanks you helped me !!
thanks you helped me too
To calculate the time spent traveling through the smaller cities, we need to determine the distance covered at 20 mph.
We start by calculating the distance covered at 80 mph. The total distance between the two major cities is given as 360 miles, and since the train travels at 80 mph in the country, we divide the distance by the speed:
360 miles / 80 mph = 4.5 hours
This tells us that the train spends 4.5 hours traveling at 80 mph.
Next, we calculate the distance covered at 20 mph. The train travels at this speed when passing through the smaller cities. We already know that the total distance is 360 miles, and we've already accounted for 4.5 hours spent at 80 mph. So, to calculate the distance covered at 20 mph, we subtract the distance covered at 80 mph from the total distance:
360 miles - (80 mph * 4.5 hours) = 360 miles - 360 miles = 0 miles
This means that the train doesn't travel any distance at 20 mph, as there are no smaller cities along the route. Therefore, the answer is zero hours spent traveling through the smaller cities.