Question Number 1: Elvin drove halfway from Ashton to Dover at 40 mph and the rest of the way at 60 mph. What was his average speed for the whole trip? (Hint: Let the distance for the whole trip be, say, 100 miles)
Let the entire distance be, say 100 miles.
For the entire trip —->
Average Speed = Distance / Time
Average Speed = 100 miles / Time
If we can find the time taken for the entire trip then we can plug it in the above equation and get the Average Speed.
Time taken for the entire trip = time taken from Ashton to Dover + time taken for the rest of the trip
= 50 miles/40 miles/hr + 50 miles/60 miles/hr
= 5/4 hr + 5/6 hr
= 25/12 hr
Now plug this time into the first formula
Average Speed = 100 miles / 25/12 hr
= 48 miles/hr
Question Number 2: A town’s old street sweeper can clean the streets in 60 hours. The old sweeper with a new sweeper can clean the streets in 15 hours. How long would it take the new sweeper to do the job alone?
Let the new sweeper do the job alone in x hours
Old Sweeper in 1 hr will do 1/60th work
New Sweeper in 1 hr will do 1/x work
So, in they work together they will do 1/60 + 1/x = 1/15
x = 20 hrs