Question

8 eric drove to his grandmothers house yesterday to visit her. he left his home at 08:45 and arrived back at 20:25. due to heavy traffic, the journey home took 40 minutes longer than the outward journey. travelling occupied 60% of the time he was away from home. at what time yesterday did eric leave his grandmothers house to drive home? 3

Explanation:

Step1: Calculate total time away

Total time from 08:45 to 20:25 is 11 hours 40 minutes, which converts to $11\times60 + 40 = 700$ minutes.

Step2: Find total travel time

Travel time is 60% of total away time:
$\text{Total travel time} = 0.6\times700 = 420$ minutes

Step3: Define variables for journeys

Let $t$ = outward journey time (minutes). Return journey time = $t + 40$.
Set up equation: $t + (t + 40) = 420$

Step4: Solve for outward time

Simplify equation:
$2t + 40 = 420$
$2t = 420 - 40 = 380$
$t = \frac{380}{2} = 190$ minutes = 3 hours 10 minutes

Step5: Calculate arrival time at grandma's

Add outward time to departure time:
08:45 + 3 hours 10 minutes = 11:55

Step6: Calculate return departure time

Total time at grandma's = total away time - total travel time = $700 - 420 = 280$ minutes = 4 hours 40 minutes
Add this to arrival time:
11:55 + 4 hours 40 minutes = 16:35

Answer:

16:35 (or 4:35 PM)