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.
