+1712 3) With a headwind, a plane traveled 840 miles northward in 2 hours. With the same wind as a tail wind, the return trip took 1 hour and 45 mineutes. Find the plane's airspeed and the wind speed.
for 3), I attempted this problem by simply making a graph... I got confused...
4) With a tailwind, a small plane traveled 420 miles in one hour and 30 min. The return trip took 30 min longer. Find the wind speed and airspeed of the plane...
for 4) I plugged in random numbers for both... I think I made the wrong equation... PLS HALP
+36916 Rate x time = distance
Rate = Speed + wind or speed - wind
speed-wind * 2 = 840
Speed + wind * 1.45 = 840 Two equations with two unknowns
From first equation W+420 =S Sub in to the second equation
(W+420+W)*1.45 = 840
W= 30 mph
Sub this result in to one of the equations to solve for S
S-30 * 2 = 840 S = 450 mph
EP: How did you get:
(W+420+W)*1.45 = 840
W= 30 mph ???
1 hour and 45 minutes =1 hour + 45/60 =1.75 -An hour and three-quarters. Why did you multiply by 1.45 ???.
Your W works out =2310 /29 =~79.65 ???
+36916 That was just a typo 1.45 should be 1.75 or 1:45 answer does not change....when I calculated it I used 1.75 but I typed 1.45
+33615 Perhaps the following will make it clearer:
EP made the trivial mistake of setting 1 hour 45 mins (i.e. one and three quarter hours) as 1.45 hours rather than 1.75 hours
Now see how you get on with your question 4) .
+128470 3) With a headwind, a plane traveled 840 miles northward in 2 hours. With the same wind as a tail wind, the return trip took 1 hour and 45 mineutes. Find the plane's airspeed and the wind speed.
Note....1hr 45 min = 1.75 hrs
Let the speed of the plane in still air be S
Let the wind speed be W
Against the wind the plane's rate is (R - W) ....the wind slows the plane's normal speed
With the wind the plane's rate is (R + W).....the wind increases the plane's normal speed
So..... Rate * Time = Distance and we have that
(R -W) * 2 = 840 ⇒ 2R - 2W = 840 ⇒ R - W = 420 ⇒ R = 420 + W (1)
(R + W) *1.75 = 840 ⇒ 1.75 R + 1.75W = 840 (2)
Sub (1) into (2) for R and we have that
1.75(420 + W) + 1.75W = 840
735 + 1.75W + 1.75W = 840
735 + 3.5W = 840 subtract 735 from both sides
3.5W = 105 divide both sides by 3.5
W = 30 mph = wind speed
And using (1) the plane's speed is 420 + 30 = 450 mph
+128470
4) With a tailwind, a small plane traveled 420 miles in one hour and 30 min. The return trip took 30 min longer. Find the wind speed and airspeed of the plane...
This one is similar to (3)
1hr 30 min = 1.5 hrs.....so
(R + W) * 1.5 = 420 (1)
(R-W ) *2 = 420 ⇒ 2R - 2W = 420 ⇒ R - W = 210 ⇒ R = 210 + W (2)
Sub (2) into (1) for R and we have that
(210 + W + W) * 1.5 = 420
(210 + 2W) * 1.5 = 420
315 + 3W = 420 subtract 315 from each side
3W = 105 divide both sides by 3
W = 35 mph
And using (1) , R = 210 + 35 = 245 mph
