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------------------------------------------------ Given the scenario is inversely proportional:

If Thando travels at a speed of 100 km/h and his journey takes him 40 minutes the first time, how long will the same journey take if he travels at 80 km/h the second time?

Answer :

It will take Thando approximately 50 minutes to complete the journey if he travels at 80 km/h.

When the speed increases (from 80 km/h to 100 km/h), the travel time should decrease to maintain a constant product.

Conversely, if the speed decreases (from 100 km/h to 80 km/h), the travel time should increase to maintain the same product.

Finding the New Time:

Let T2 be the unknown travel time when the speed is 80 km/h. We know the initial speed (S1) is 100 km/h, and the initial time (T1) is 40 minutes (which we need to convert to hours first).

1. Convert Minutes to Hours:

40 minutes = 40/60 hours = 2/3 hours (since 60 minutes are in 1 hour)

2. Constant Product Relationship:

Since speed and time are inversely proportional, their product remains constant:

S1 * T1 = S2 * T2

where:

S1 = Initial speed (100 km/h)

T1 = Initial time (2/3 hours)

S2 = New speed (80 km/h)

T2 = Unknown new time

3. Solving for T2:

Plug in the known values and solve for T2:

(100 km/h) * (2/3 hours) = (80 km/h) * T2

Rearranging the equation:

T2 = (S1 * T1) / S2

T2 = [(100 km/h) * (2/3 hours)] / (80 km/h)

4. Simplifying and Calculating:

T2 = (200 hours * km) / (240 km/h) [We can cancel out km units]

T2 = 5/6 hours (or 50 minutes since 1 hour = 60 minutes)

Therefore, it will take Thando approximately 50 minutes to complete the journey if he travels at 80 km/h.

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