Question

L and ben are drivers for sd trucking company. one snowy day, ben left sd at 8:00
a.m. heading east and al left sd at 11:00
a.m. heading west. at a particular time later that day, the dispatcher retrieved data from sd's vehicle tracking system. the data showed that, up to that time, al had averaged 40 miles per hour and ben had averaged 20 miles per hour. it also showed that al and ben had driven a combined total of 240 miles. at what time did the dispatcher retrieve data from the vehicle tracking system

Answer 1

Alright, lets get started.

Ben left at 8:00 AM and Al left at 11:00 AM.

Suppose dispatcher retrieves data after t hrs when Al left SD.

We know the average speed of Al = 40 miles per hr

So, distance covered by Al = Time * speed

Distance covered by Al = 40 t

We know average speed of Ben = 20 miles per hr

As we know Ben left SD 3 hrs before, time taken by Ben will be 3 hrs higher than AL means (t+3)

So distance covered by Ben = $20 (t + 3)$

Total distance covered by both will be = $40 t + 20 (t+3)$

Total distance covered by both will be = $40 t + 20 t + 60$

Total distance covered by both will be = $60 t + 60$

But as per given in question, total distance covered by both is 240 miles.

Hence making both equal,

$60 t + 60 = 240$

Subtracting 60 from both sides

$60 t + 60 - 60 = 240 - 60$

$60 t = 180$

Dividing 60 in both sides

$\frac{60 t }{60} = \frac{180}{60}$

t = 3 hrs

It means it was 11:00 AM + 3 hrs means 2:00 PM when dispatcher retrieve data. : Answer

Hope it will help :)