Did I do anything wrong so far?
by admin on Saturday, December 18th, 2010 | 3 Comments
Two camper vans leave Arrowhead Lake at the same time, one traveling north at a speed of 10km/h faster than the other, which is traveling south. Afer 3 hours, the camper vans are 420 km apart. Find their speeds.
For one van, I put that the rate is r + 10, the time is 3 h, and the distance is 420km.
For the other van, I put that the rate is r, the time is 3 h, and the distance is 420.
I know they travel 65km and 75km seperately, but I think I did something with the rates, times, and distances. What’d I do wrong?
And when I say 65km and 75km/h seperately, I mean that one van goes 65km and the other van goes 65km/h.
The 420 is the result of both vans separating. It is not the distance of each van.
The distance between the two vans increases at the rate of:
Speed of van 1 + speed of van 2 = [(r+10) + r]*3 = 420
If you want ot use your approach (which is OK, except for where you put the 420), you’d have something like.
Van number 1 goes north at a speed of (r+10);
after 3 hours, it will have gone a distance of 3(r+10)
Van number 2 goes south at a speed of r;
after 3 hours, it will have gone a distance of 3r
The distance separating them is:
3(r+10) + 3r = 450
The distance between them is 420 km so write
dN = (r+10)*10 for the vehicle going north and
dS=-r*3 for the south going vehicle
The distance between them is then
420 = dN – dS = (r+10)*3 + r*3
which you can solve for r
theres actually a really simple way to do this without d = r x t and combining two equations:
you just say that the (10mph)(r)(3hours) is the only difference between them, so 30r= 420.
420/3=140. so 140 mph is the answer.