# Speed Time and Distance

#### zidan3311

hello all...

i have a question :

"John riding a bike from city A to city B. He departed at 07.00 am with speed of 60 kmph . From town A , Sisca followed with a speed of 80 kmph , what time Sisca followed John ?

a) 10.00 am
b) 11.00 am
c) 12.00 am
d) 13.00 am

how to solve this problem with quickly method.

could you help me?

zidan3311

#### chiro

MHF Helper
Hey zidan3311.

I think you should look at functions given different time intervals.

You have time in terms of minutes or hours (or something else). If t = 0 then you let that be at some point (like 7am).

Note that distance = speed * time. You have information of speed and you need distance. You have two equations - one for each rider.

See if you can get some formulas using this information.

• 1 person

#### zidan3311

could you to explain to me with sample number look like my case?

#### chiro

MHF Helper
So we have a simple relation that distance = speed * time.

If we have speed in terms of x km/h and our time is in hours then after t hours we have

distance = x * t where x and t are as above. For 0 hours we have

distance = x * 0 = 0 km which is expected. After one hour we have

distance = x * 1 = x km which is expected. In your case one of your speeds is 60km/h so we have for 1 hour a distance of

distance = 60 * 1 = 60km.

Now you have two different formulas for each bike rider. Note that if one rider started later at some time t0 then you would "shift" your formula to take that into account.

So if one rider started at t = 0 your formula would be distance = speed * t. If you have somebody start at time t0 after the first rider started your formula for distance would be

distance_2 = speed_2 * (t - t0) where t0 is the time the second one started (in hours).

Combining both of these together you have two formulas for the two riders:

distance_1 = speed_1 * time
distance_2 = speed_2 * (time - t0) where t0 is when the second rider starts riding.

You are given both speeds in km/h and your times will be in hours while your distances will be in km.

You need to solve for the times and you will need to figure out the distances to do that.

• 1 person

#### zidan3311

i try like this :

#### zidan3311

i have try, but still not working..

could you make more simple explanation, i mean with sample case...

#### votan

hello all...

i have a question :

"John riding a bike from city A to city B. He departed at 07.00 am with speed of 60 kmph . From town A , Sisca followed with a speed of 80 kmph , what time Sisca followed John ?

a) 10.00 am
b) 11.00 am
c) 12.00 am
d) 13.00 am

how to solve this problem with quickly method.

could you help me?

zidan3311
There is no such a time 13:00 am. eliminate this from your possible answer
Starting at 12:00 am means the second bicker started 7 hour before the second bicker, contrary to the question. Eliminate this as a possible answer
You are left to choose between 11:00 am and 10:00 am. These are not the times to include in your equations.

Start by saying the two bickers covered the same distance. The fasted way you asked for is to find how many hours each bicker spent on the road.

Notice that 3*80 = 4*60 = 240 km

That means the first bicker spent 4 hours on the road to reach the encounter location. That was at 7 + 4 = 11:00 am
The second bicker spent only 3 hours to reach the encounter location. It must have started 1 hour afterward at 8 + 3 = 10:00 am

• 1 person

#### zidan3311

There is no such a time 13:00 am. eliminate this from your possible answer
Starting at 12:00 am means the second bicker started 7 hour before the second bicker, contrary to the question. Eliminate this as a possible answer
You are left to choose between 11:00 am and 10:00 am. These are not the times to include in your equations.

Start by saying the two bickers covered the same distance. The fasted way you asked for is to find how many hours each bicker spent on the road.

Notice that 3*80 = 4*60 = 240 km

That means the first bicker spent 4 hours on the road to reach the encounter location. That was at 7 + 4 = 11:00 am
The second bicker spent only 3 hours to reach the encounter location. It must have started 1 hour afterward at 8 + 3 = 10:00 am

hi Votan...

i'am sorry there is something wrong with my question, the should be :

"John riding a bike from city A to city B. He departed at 07.00 am with speed of 60 kmph . From town A , Sisca followed with a speed of 80 kmph at 08.00 am, what time Sisca followed John ?

the answer should be : 11.00 am

how to make it easy & possible using ratio approach :
maybe like 7 am --------60 kmph
8 am --------80 kmph

what's formula?

#### zidan3311

hi..

the new similar problem :

A bus departs from city X at 07:55 am with speed of 80 kmph . and A truck departs from the city of Y at 08:10 am with a speed of 100 kmph. Two cities 260 km distance. At what time did they meet?

do you have brilliant ideas?

#### zidan3311

the should be answer : 09.30 am..

How to Find it?