maths problem, help is needed!!!!!!!!!!!?

Question

Two ships, the Algoa and the aTitanium are preparing to leave harbor. The Algoa leaves the harbor 15 minutes before the Titanium. The Algoa travels at 24km/h and the titanium at 28km/h. After how many hours will the two ships meet???????

Answer 1

Hi,

First, the Algoa got a 15 minute head start. That is ¼ of an hour. Since distance = rate x time, then the Algoa's rate x Algoa's time = Titanium's rate x Titanium's time. If x = Titanium's time after it started, then x + ¼ is the Algoa's time. The equation for this is:

24(x + ¼) = 28x
24x + 6 = 28x
6 = 4x
1½ = x

If would be 1½ hours after the Titanium left port that they would have traveled the same distance along the same course. This is also 1¾ hours after the Algoa had set sail.

I hope this helps!! :-)

Answer 2

Speed of Algoa = SA = 24 km/h
Speed of Titanium = ST = 28 km/h
Let's call the time (in hours) when the ships meet H. Let's start timing H from the time Titanium starts moving. (Means we'll add in the 15 minutes somewhere else)
The ships meet when they both go the same distance.

In H hours Algoa will be how far from port? = 24 x H plus the distance she went in her 15 minute head start. (15 mins is 1/4 hr so 24 km/h x (1/4)h = 6 km) so Algoa distance = 24 x H + 6
and Titanium will be 28 x H km

So, fine the value for H where
24H + 6 = 28H
or 4H = 6
H = 6/4 = 3/2
H = 1 hr and 30 minutes (1 and 1/2 hours)

Answer 3

Ship A leaves 15 mins early @ 24 km/h
means she is ahead 25% or 6 km

difference between ship's speeds is 4 km

6 div by 4 = 1.5 hours to catch up

tada!!

Answer 4

A ------B------C

A IS HARBOR
B IS SOME MIDDLE POINT WHERE ALGOA REACHES AFTER 15 MINS AND AT THAT TIME TITANIUM TAKES OFF FOR THE SEA.
C IS THE POINT WHERE ALGOA AND TITANIUM MEET.

WELL YOUR ANSWER CAN BE EXPLAINED ON THE BASIS OF ALGEBRA

SOLUTION:
ALGOA START FROM POINT A.
algoa reaches point B after 15 MINS i.e converting into hour =15/60 =0.25 hours.
then let algoa take T hours to reach from point B to point C which is also the time taken by titanium to reach from point A to point C where algoa and titanium meet.

thus distance =speed x time -- for Algoa
so distance AB= 24 x 0.25 = 6 km
distance BC =24 x T km.
therefore AC=AB+BC =6 +(24XT) KM.

Now since titanium meets algoa at point C
It takes same T hours for titanium to reach from point A to point C therefore it coverss a distance AC =speed x time
which is 28 xT .-- for titanium
therefore

6 +(24 x T) =28 x T
solving equation 1 for T
we get T= 1.5 Hours. which is the time taken by titanium to reach from point A to point C and thus algoa takes 1.5 hours t o reach from point B to point C and a total of 1 hour 45 mins to reach from point A to point C

Answer 5

a=algoa
t=titanium

V=D/T

Va=24 Km/h
Vt=28 Km/h

15 minutes=0.25 hours

Ta-0.25=Tt

D is the same for both because they "meet" (Da=Dt=D)

So, because:

Va=D/Ta
Vt=D/Tt

So Va*Ta=Vt*Tt
Va*Ta=Vt*(Ta-0.25)
24Ta=28Ta-28*0.25
4Ta=28*0.25
Ta=7*0.25
Ta=1.75 hours

The 2 ships will meet after 1.75 hours the Algoa has departured

After note:

KRYPTON: Don't get confused. Other answerers are right also by saying 1.5 Hours but that is the time since the last departure (Titanium). So it depends on how you answer (1.5 hours after the last ship departed or 1.75 hours since the first departure).

Answer 6

x=24*0,25+t*24
x=28*t

t=24/8=3 hours.

Answer 7

6.

Answer 8

after one and a half hour