# Two trains

Through the bridge, long l = 240m, the train passes through the constant speed at time t1 = 21s. A train running along the traffic lights at the edge of the bridge passes the same speed at t2 = 9s.

a) What speed v did the train go?
b) How long did it take for a train driver to cross the bridge?
c) What is the L train length?
d) How long will it take for a train to overtake in the same direction with the same length but half the speed?
e) How long will it take for a train to overtake in the opposite direction with the same length but half the speed?

Result

v =  20 m/s
L =  180 m
t3 =  12 s
t4 =  36 s
t5 =  12 s

#### Solution:

$l = 240 \ m \ \\ t_{ 1 } = 21 \ s \ \\ t_{ 2 } = 9 \ s \ \\ \ \\ \ \\ L = 9 \cdot \ v \ \\ \ \\ L+240 = 21 \cdot \ v \ \\ \ \\ \ \\ \ \\ L-9v = 0 \ \\ \ \\ L-21v = -240 \ \\ \ \\ \ \\ \ \\ L = 180 \ \\ \ \\ v = 20 \ \\ = 20 \ \text { m/s }$
$L = 180 = 180 \ \text { m }$
$t_{ 3 } = l/v = 240/20 = 12 = 12 \ \text { s }$
$t_{ 4 } = \dfrac{ 2 \cdot \ L }{ v-v/2 } = \dfrac{ 2 \cdot \ 180 }{ 20-20/2 } = 36 = 36 \ \text { s }$
$t_{ 5 } = \dfrac{ 2 \cdot \ L }{ v+v/2 } = \dfrac{ 2 \cdot \ 180 }{ 20+20/2 } = 12 = 12 \ \text { s }$

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Be the first to comment!

#### Following knowledge from mathematics are needed to solve this word math problem:

Do you have a linear equation or system of equations and looking for its solution? Or do you have quadratic equation? Do you want to convert length units?

## Next similar math problems:

1. The tourist
The tourist traveled 78km in 3 hours. Part of the journey went on foot at 6km/h, the rest of the trip by bus at 30km/h. How long did he walk?
2. Wavelength
Calculate the wavelength of the tone frequency 11 kHz if the sound travels at speeds of 343 m/s.
3. Aircraft nose down
How long will fall airliner from a height of 10000 m at speed 1,000 km/h?
4. Walkers
From points A and B simultaneously started against each other two walkers. After meeting both continue to B. Second walker came to B 2 hours before the first walker. It's speed is 2.7 times of speed of the first pedestrian. How many hours went pedestria
5. Two planes
Two planes flying from airports A and B, 420 km distant against each other. Plane from A took off 15 minutes later and flies at an average speed of 40 km/h higher than the plane from B. Determine the average speed of this two aircraft if you know that it
6. Car and motorcyclist
A car and a motorcyclist rode against each other from a distance of 190 km. The car drove 10km/h higher than the motorcyclist and started half an hour later. It met a motorcyclist in an hour and thirty minutes. Determine their speeds.
7. Pooja
Pooja and Deepa age is 4:5, 4 years back it was 8:11. What is the age of Pooja now?
8. Sebastian
From Kovalov Sebastian walks at 6 km / h started at 8:00 in the direction of Kuty. From Kuty, the godfather is driving at 50 km/h and started at 8:30. The distance is 24 km. When and where grandfather will take Sebastian to the car.
9. Carla
Carla is 5 years old and Jim is 13 years younger than Peter. One year ago, Peter’s age was twice the sum of Carla’s and Jim’s age. Find the present age of each one of them.
10. Three unknowns
Solve the system of linear equations with three unknowns: A + B + C = 14 B - A - C = 4 2A - B + C = 0
11. Lee is
Lee is 8 years more than twice Park's age, 4 years ago, Lee was three times as old. How old was Lee 4 years ago?
12. Legs
Cancer has 5 pairs of legs. The insect has 6 legs. 60 animals have a total of 500 legs. How much more are cancers than insects?
13. Elimination method
Solve system of linear equations by elimination method: 5/2x + 3/5y= 4/15 1/2x + 2/5y= 2/15
14. Distance between two cities
Car went from A to B 4h. On the way back, the car was up 15km / h faster. The return trip took 48 minutes. Shorter than the way there. Find the distance of the cities A and B.
15. Men, women and children
On the trip went men, women and children in the ratio 2:3:5 by bus. Children pay 60 crowns and adults 150. How many women were on the bus when a bus was paid 4,200 crowns?
16. Children
The group has 42 children. There are 4 more boys than girls. How many boys and girls are in the group?
17. Ball game
Richard, Denis and Denise together scored 932 goals. Denis scored 4 goals over Denise but Denis scored 24 goals less than Richard. Determine the number of goals for each player.