1. Elvin drove halfway from Ashton to Dover at 40 mi/h and the rest of the way at 60 mi/h. What was his average speed for the whole trip? (hint: let the distance for the whole trip be, say, 100 mi.)
2. A train averaged 120 km/h for the first two thirds of a trip and 100 km/h for the whole trip. Find its average speed for the last third of the trip.
3. Pipe A can fill a tank in 5 hours. Pipe B can fill it in 2 hours less time than it takes pipe C, a drainpipe, to empty the tank. With all three pipes open, it takes 3 hours to fill the tank. How long would it take pipe C to empty it?
2007-12-04 08:53:20 · 3 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
PROBLEM 1:
The hint is useful otherwise you might assume the answer was 50 mph...
Let T be the time for the first half of the trip.
50 = 40 T
T = 50/40 = 5/4 = 1 1/4 hours
Let T2 be the time for the second half of the trip:
50 = 60 T
T = 50/60 = 5/6 hours
Adding the time together we have 5/4 + 5/6 = 15/12 + 10/12 = 25/12 hours
100 miles = R * 25/12
R = 100 * 12/25
R = 4 * 12
R = 48
So his average speed is 48 mph
2007-12-04 08:59:17 · answer #1 · answered by Puzzling 7 · 0⤊ 0⤋
1) Better yet, make the distance 240 miles (half of which is a multiple of both 60 and 40). The first half (120 miles) he drove in three hours and the second half he drove in 2 hours. Thus, his average speed is 240 miles divided by 5 hours = 48 miles/hour.
2) This question is imprecise. When you say "two thirds", is that 2/3 of the total time spent on the trip or 2/3 of the distance traveled?
2007-12-04 08:57:53 · answer #2 · answered by smcwhtdtmc 5 · 2⤊ 0⤋
50/40 = 5/4 hours
50/60 =5/6 hours
total time = 5/4+5/6 =25/12 hours
100/(25/12) = 48 mph
Assume distance = 360 km
240/120 = 2 hours
360/100 =3.6 hours
So last 1/3 took 1.6 hours
So 120/1.6 = 75km for laast 1/3 of trip
2007-12-04 09:35:13 · answer #3 · answered by ironduke8159 7 · 0⤊ 0⤋