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Texas Instruments technical mcq question, verified with a worked answer. Free to practise - no sign-up.
Vehicle tracking devices**
Mr. Park has two drivers A and B, who drive two different cars. He has installed a vehicle tracking device in both vehicles. On a particular day, Driver B left at 10:00 a.m. heading south, and driver A left at 2:00 p.m. heading north.
Later that day, at a particular time, data was retrieved from both the tracking devices. It showed that, up to that time, A had averaged 60 miles per hour, and B had averaged 40 miles per hour. It also showed that A and B had driven a combined total of 460 miles.
At what time was the data retrieved from the vehicle tracking devices?
Show answer & explanation
The total distance is the sum of the distances traveled by Driver A and Driver B. By setting up an equation based on their respective travel durations relative to the retrieval time, we find that 5 hours after Driver A started (5:00 PM) satisfies the total distance of 460 miles.
Step-by-step Derivation:
Step 1: Define the retrieval time as T (in hours since 10:00 AM).
Step 2: Calculate the travel time for Driver B. Driver B started at 10:00 AM, so B's travel time is T hours.
Step 3: Calculate the travel time for Driver A. Driver A started at 2:00 PM, which is 4 hours after 10:00 AM. So, A's travel time is (T - 4) hours.
Step 4: Use the distance formula (Distance = Speed × Time).
Distance B = 40 * T
Distance A = 60 * (T - 4)
Step 5: Set up the equation for the combined total distance:
40T + 60(T - 4) = 460
Step 6: Solve for T:
40T + 60T - 240 = 460
100T = 460 + 240
100T = 700
T = 7 hours.
Step 7: Determine the retrieval time. 7 hours after 10:00 AM is 5:00 PM.