Andrew M. answered • 02/28/20
Experienced Math Tutor and Engineer Specializing in Upper Level Math
We need to use Liam's speed and time taken to figure out how far he has traveled and how long it took him to get there and use that data to set up a linear equation for Tobias since Tobias rode at a constant speed. We can then use that equation to figure out what time he reaches his destination.
If Liam rides at a rate of 15km/h for 10km between each break, 10/15 = 2/3 and 2/3 of an hour is 40 minutes. So we know each leg of his trip is 40 minutes. We know Tobias catches up after his third break so 40(3) = 120 minutes. We know he also spent 10 minutes on each break so that's another 30 minutes. In total, Liam spent 150 minutes to get to the point that Tobias caught up to him but Tobias started riding an hour after Liam. So 150 - 60 = 90 minutes. Their distance traveled would be the same though. Since the distance traveled during Liams breaks are 0, we only need to add up the 3 times he rode 10km so in total, the two traveled 30km to reach this point.
We now know that Tobias traveled 30km in 90 minutes so we can set up a linear equation for his speed. Since we can say his starting point to be 0, we only need to find the slope of the equation since the y-intercept will be 0.
30km/1.5hr = 20km/h (note: converted 90 minutes to 1.5 hours to get km/h)
So the equation for Tobias's speed is y = 20x where y is distance traveled and x time spent riding. We know that he rode 40 miles in total so we can plug in y = 40 and solve for x to find how long it took him to cover that distance in hours.
40 = 20x, Thus
x = 2
It took Tobias 2 hours from when he left to reach his destination. Since he left at 8 am, Tobias reached his destination at 10 am
