Motion problem! i dont get it! ;'(?

Question

Uhm here's the problem: A train left the station at 9 am traveling at 50 mph. AT 11 pm, an airplane left the same place in the same direction at 175 mph. AT what time will the plane overtake the train? Can someone also tell me the steps? Thankshoo. :*

Answer 1

The train leaves 14 hours earlier than the plane. By the time the plane takes off, the train would have covered 14*50 = 700 miles.

The relative velocity of the plane to the train is (175-50) = 125 mph.

What you need to do now is work out how long it would take to cover 700 miles at a speed of 125 mph:
700miles/125mph = 5.6 hours or 5 hours and 36 minutes.

The plane will overtake the train 5 hours and 36 minutes after it takes off or at 4:36am.

Answer 2

At 11pm, D of train = 50 ( 14) = 700 miles
From then on, the plane is gaining (175 - 50 = 125 mph).
To gain 700 mi the plane needs 700/125 = 5.6 hrs
Therefore the plane will overtake the train at 4:36 am the following day.

Answer 3

After 14 hours train travels 700 miles
Relative speed of plane to train = 125 mph
t = 700 / 125 h
t = 28 / 5 h
t = 5 h 36 min
Plane takes off at 11 pm
Will overtake at 04:36

Answer 4

*hi,
Let the time when the plane will overtake the train be 't'.
Also we know that the time 't' is greater than 14 hours i.e. the difference between the two times.

so, distance covered by train till the 't' th hour is,
dist = (t - 9)*50
and the distance covered by plan till the 't' th hour is,
dist= (t - 23)*175 converting 11pm to 23 rd hour

so, since the dist will be same when the plane overtakes the train.

(t - 9)*50 = (t - 23)*175
(t - 9)*2 = (t - 23)*7
2t - 18 = 7t - 161
5t = 143
t = 28.6
i.e the plane will overtake the train at 4:36 am the next day.

Note: 28.6 = 24 + 4.6
now, 4.6 is 4 hours and 36 minutes.

Hope, I helped you.

Answer 5

From 9 AM to 11 PM (14 Hrs) the train has covered a distance of (Vel. x Time) = 50 x 14 = 700 miles.
At 11 PM the plane starts with 175mph.
At 11 PM the distance between train & plane = 700 miles
Now we have to consider the relative velocity to cover the distance 700 miles, as both train and plane are in motion.
As both of them are in the same direction their relative velocity will be the difference of their velocities.
R.V = 125 mph
Distance = 700 miles
Time to overtake = Distance / Velocity
... . . . . . . . ... ....= 700/1125 = 5.6 hrs = 5 hrs 36 min
. . . . . . . . . . . . . .===============================
Verification:
Train travels for (14+5.6) hrs at 50 mph=19.6 x 5.6=980 miles
............... ......................... ......................... .........==========
Aeroplane flies for 5.6 hrs at 175 mph = 5.6 x 175 =980 miles
..................... ................. ....................... ...........==========
The plane will overtake the train at 04.36 AM next day

Answer 6

Set up two equations one for the train and one for the plane, set them equal to each other and solve for the time.

distance for train = (50mph)(14hrs) + (50mph)t

distance for plane = (175mph)t

50 x 14 +50t = 175 t

700 = 125 t

700/125 = t

t= 5.6 hrs or 4:36A.M.

Answer 7

Train Distance (Xt) =train velocity (Vt) * train Time(Tt)
Xt=Vt*Tt
Airplane distance(Xa) = airplane Velocity(Va) x airplane time(Ta)
Xa=Va*Ta
airplane time (Ta)=Train time(Tt) - 2 hrs
Train Distance(Xt) = airplane distance(Xa)
Xt=Vt*Tt = Xa = Va*Ta
Vt*Tt=Va*Ta
Since Ta=Tt-14
Vt*Tt=Va*(Tt-14)
Vt*Tt=VaTt-14va
50*Tt=175*Tt-2450
Tt=19.6 Hrs
Ta=19.6-14=5.6 hr=336 min its will over take the train at 4:36 am