Question 1207036
<br>
Let x be the number of hours the trip takes at 48km/hr.<br>
Then, since the arrival time at the lower speed is 2 hours later, x+2 is the number of hours it takes at 40km/hr.<br>
The distances at the two speeds are the same:<br>
48(x) = 40(x+2)
48x = 40x+80
8x = 80
x = 10<br>
The trip at 48km/hr takes 10 hours, so the distance is 48*10 = 480km.<br>
ANSWER: 480km<br>
Here is a quick informal way to solve the problem mentally, if your mental math is good....<br>
The ratio of the two speeds, as a fraction, is 40/48.<br>
The distances are the same, so the ratio of the times is the same as the ratio of the speeds.<br>
Since the difference in the times is 2 hours, write the ratio 40/48 as an equivalent fraction in which the difference between the numerator and denominator is 2: 40/48 = 10/12.<br>
So the trip takes 12 hours at 40km/hr or 10 hours at 48km/hr, making the trip 480km.<br>