1 hour after 2.20 p.m. will be 3.20 p.m.

We are then left with 50 minutes to add to the 3.20 p.m.

If you add 40 minutes to the 20 minutes after the 3 p.m. [3.20 p.m.] that will be 1 hour [60 minutes make an 1 hour] and at that time the time will be 4 p.m. [1 hour after 3.00 p.m.] and the 50 minutes will be left with 10 minutes.

10 minutes after 4.00 p.m. is 4.10 p.m.

Hence the match will end at 4.10 p.m.

ALTERNATIVELY

To add time, add the hours separately and the minutes separately

If the minutes is 60 or more, convert to hours and minutes

2.20 p.m. = 2 hours and 20 minutes

Adding 1 hour 50 minutes

Adding Hours

2 + 1 = 3

Adding Minutes

20 minutes + 50 minutes = 70 minutes

60 minutes make an hour, hence 70 minutes is 1 hour 10 minutes

Add the 1 hour to the previous sum of the hours

Total hours = 3 + 1 = 4

Minutes left is 10 minutes

Hence the match ends at 4.10 p.m.

Speed = Distance/Time

Since the unit is metres per second, convert the kilometres to meters and the hour to seconds

Kilo = 1000, kilometres = 1000 metres

36 kilometres = 36 000 metres

60 minutes = 1 hour

1 minute = 60 seconds

60 minutes = 60 x 60 seconds = 3600 seconds = 1 hour

Speed = 36 000m / 3600s = 10 ms^-1

You can make time the subject of the equation

Since time is dividing, you can multiply both sides of the equation by time to cancel the time at the right hand side

Time x Speed = Distance

Divide both sides by Speed

From the question, distance covered = 150 km

Speed was 18 km/h

Time = 150/18

3 goes into 150, 50 times and 18, 6 times

Time = 50/6

2 goes into 50, 25 times and 6, 3 times

Time = 25/3

3 can go into 25, 8 times remainder 1

Time = 8 1⁄3 hours, thus 8 whole number 1 over 3

You can change the fraction part of the hours to minutes by multiplying by 60 minutes. There are 60 minutes in an hour

1⁄3 hours = 1⁄3 x 60 minutes = 20 minutes

Therefore the time taken is 8 hours 20 minutes

speed = distance/time

speed = 18 km/h and time = 8 h

Subsituting speed and time in the speed equation above,

⇒ 18 km/h = distance/8 h

Make distance the subject. Since 8h is dividing, multiply both sides by 8h

⇒ 8h x 18 km/h = 8h x distance/8 h, 8h cancels each other leaving distance alone at the right side of the equation.

⇒ 8 x 18 km = distance

⇒ distance = 144 km

1⁄3 = 5 km

18 cm = ?

Let 18 cm = xkm and cross multiply to solve for the value of x

1⁄3 x x = 5 x 18

Applying the principles of multiplying fractions

Every number is being divided by 1 hence x = x/1

1⁄3 x x = 5 x 18

Get rid of the fraction by multiplying both sides of the equation by the L.C.M of the denominators.

The L.C.M of 3 and 1 is 3, hence multiply both sides of the equation by 3

x = 270

Alternatively

You can cross multiply and solve for the value of x

x x 1 = 90 x 3

x = 270

Alternatively, you can calculate how many times 1⁄3 can go into 18 and multiply the result by 5 km

Applying the principles of dividing fractions

Thus when dividing fractions, you reverse the fraction at the right and change the division to multiplication

Now you can use the principles of multiplying fractions to simplify

Every number is being divided by 1

From 9:45 am to 12 pm is 2 hours 15 minutes

Notes:

1. 9:45 am + 2 hours = 11:45 am
2. From 11:45 am to 12 pm is 15 minutes

From 12 pm to 4:15 pm is 4 hours 15 minutes

Total hours = 2 hours + 4 hours = 6 hours

Total minutes = 15 minutes + 15 minutes = 30 minutes

Time spent = 6 hours 30 minutes

Method I

Using formula

Distance covered by 20 km/h in 35 minutes = 20 km/h x 35 minutes

Make time the subject in the speed formula.

Distance = Speed x Time

Divide both sides by Speep

Time = $\frac{\mathrm{Distance}}{\mathrm{Speed}}$

New speed = 28 km/h

Same distance = 20 km/h x 35 minutes

Time = $\frac{\mathrm{20\; km/h\; x\; 35\; minutes}}{\mathrm{28\; km/h}}$ = 25 minutes

Notes:

1. km/h cancel out
2. 4 divides 20, 5 times and 28, 7 times
3. 7 divides itself 1 and 35, 5 times
4. 5 x 5 = 25

Method II

Since distance (speed x time) is the same:

Speed₁ x Time₁ = Speed₂ x Time₂

Speed₁ = 20 km/h

Time₁ = 35 minutes

Speed₂ = 28 km/h

Substituting into the equation:

20 km/h x 35 minutes = 28 km/h x Time₂

Divide both sides by 28 km/h

Time₂ = $\frac{\mathrm{20\; km/h\; x\; 35\; minutes}}{\mathrm{28\; km/h}}$ = 25 minutes

Note: Speed and time are inversely proportional when the distance is constant. If speed increases, the travel time decreases.

Hence you can't use the direct proportionality to obtain the time. Using proportionality gives you 49 minutes which is incorrect