Two ships

The distance from A to B is 300km. At 7 am started from A to B a ferry with speed higher by 20 km/h than a ship that leaves at 8 o'clock from B to A. Both met at 10h 24min. Determine how far they will meet from A and when they reach the destination.

Result

s₁ =  204 km
t₁ = 12:00 hh:mm
t₂ = 15:30 hh:mm

Solution:

$$\begin{gathered} s=300\text{ km } \\ {s}_1+s_2=s \\ {s}_1=(v+20)t \\ {s}_2=v(t-1) \\ t=(10+24\mathrm{/}60)-7.00={\displaystyle \frac{17}{5}}=3.4\text{ h } \\ (v+20)t+v(t-1)=300 \\ 3.4\cdot (v+20)+v\cdot 2.4=300 \\ 5.8v=232 \\ {\displaystyle \frac{29}{5}}v=232 \\ 29v=1160 \\ v=1160\mathrm{/}29=40 \\ {s}_1=(v+20)\cdot t=(40+20)\cdot 3.4=204\text{ km} \end{gathered}$$

$t_1=7.00+s\mathrm{/}(v+20)=7.00+300\mathrm{/}(40+20)=12=12:00\text{ hh}:\text{mm}$

$t_2=8.00+s\mathrm{/}v=8.00+300\mathrm{/}40={\displaystyle \frac{31}{2}}=15.5=15:30\text{ hh}:\text{mm}$

Try another example

Showing 0 comments:

Next similar math problems:

• Two cities
  The distance between cities A and B is 132 km. At 9.00 am, the cyclist started the bike at an average speed of 24 km/h, and at 10.00 h started from the B cyclist at an average speed of 30 km/h. How long and far from A will they both meet?
• Motion 2
  At 10 o'clock started from place A car speed at 90 km/h. 20 minutes after started from the place B at speed 60 km/h another car. Distance places A and B is 120 kilometers. What time and where they meet?
• Two cities
  Cities A and B are 200 km away. At 7 o'clock from city A, the car started at an average speed of 80 km/h, and from B at 45 min later the motorcycle is started at an average speed of 120 km/h. How long will they meet and at what distance from the point A i
• Two airports
  Two airports are 2690 km away. From the first airport, the airplane flies at a speed of 600 km/h, from a second airplane at a speed of 780 km/h. When will they meet if they flew at 10:00? How far from the first airport?
• Train from Brno
  First train started from Brno at 8 am at 60 km per hour. Second train started from Opava at 7 o'clock at the speed of 40 kilometers per hour. In how many hours and how far from cities trains meet when the distance of cities is 200 kilometers.
• Cars speeds
  Distance from city A to city B is 108 km. Two cars were simultaneously started from both places. The speed of a car coming from city A was 2 km/h higher than the second car. What was the speed of each car if they met in 54 minutes?
• Two ships
  Two ships sailed from Venice - a cargo speed of 10 knots and a ferry speed of 18 knots. At what time will the ferry catch up with the cargo ship if it sailed 10 hours later?
• Znojmo
  From Znojmo to Brno started truck with a trailer at an average speed 53 km per hour. Against him 14 minutes later from Brno started car with an average speed of 1.2-times greater than the truck. How long and how far from Znojmo, they meet if the distance
• Where and when
  The truck left Kremnica at 11:00 h at a speed of 60km/h. At 12:30 h, the passenger car started at an average speed of 80km/h. How many kilometers from Kremnica will the passenger car reach truck, and when?
• Two trains
  Two trains go at each other. First at speed 40 km/h and the second at speed 60 km/h. At what distance will be 30 minutes before they will meet?
• Car - road
  Car started at 11:40 at speed 54 km/h from A and to B arrived at 12:20. Determine the distance A and B.
• Motorcyclist
  From Trutnov, the motorcyclist started at an average speed of 60km/hour. At 12.30hrs the passenger car was started at a speed of 80km/hour. How many hours and at what distance from Trutnov will car catch a motorcycle?
• Motion
  From two different locations distant 232 km started against car and bus. The car started at 5:20 with average speed 64 km/h. Bus started at 7:30 with average speed 80 km/h. When they meet? How many kilometers went the bus?
• Cyclist vs boat
  The cyclist wants to ride a short distance by boat, but when he stops at the pier, the boat does not pick up passengers yet and is preparing to leave. The cyclist decides that the boat will catch up at the next stop. The stop is 12km far along the water a
• Car and cyclist
  Cyclist started from town at speed 18 km/h. After 1 hour 30 min started the car from town and caught up with the cyclist in 50 minutes. How fast was a car?
• Cars
  Cars started at 7:00 AM. From point A car run at 40 km per hour, from B car run 70 km per hour. Between A and B is 250 km long road. When and where will meet (measured from point A)?
• Two cyclists
  Two cyclists started from crossing in the same time. One goes to the north speed 20 km/h, the second eastward at speed 26 km/h. What will be the direct distance cycling 30 minutes from the start?