LOL thanks, madam.

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Total Distance = 120 miles
Total time = 2 hr 22 mins = 142 mins

Time Taken to cover last segment of trip = 10 /50 = 1/5 hr *60 = 12 mins
Time taken to cover middle segmentrip of trip = 100 / 60 = 5/3 hr *60 =100 mins
Time Taken to cover first segment of trip = 142 - (100+12) = 30 mins = 1/2hr
Distance of cover in first segment = 10 miles
Speed = 10 / (1/2) = 20 mph

Let’s start by breaking down the problem:

We’re told the the city road is 10 miles long and travelled at an unknown average speed - let’s call that (s).

And we are told that the country road is also 10 miles but travelled at an average speed of 50 mph

Then we are told that the interstate highway is 120 miles long minus the city roads (10 miles) and minus the country roads (10 miles), which is 100 miles. We are told the average speed on the interstate is 60 mph.

We want to know Lorenzo’s average speed (let’s call that S) on the city roads.

To calculate the average speed we use the formula:
Speed = (Distance/Time)

We can now set up an equation to solve for (S).

First we will find the times spent on country road and the interstate highway.

First, let’s find the time spent on the country road:
Time = Distance / Speed
Time = 10/50 = ⅕ (hours)

Next, the highway:
Time = Distance / Speed
Time = 100/60 = 5/3 (hours)

We’re told that the total journey time is 2 hours and 22 minutes, which can be written as 2*(22/60) = 2*(11/30)

Then let’s subtract the time spent on the highway and country road to find the time spent on the city road.

2*(11/30) - (5/3) - (⅕) = 10/S (we’re told the city road is 10 miles long).

½ = 10/S

S = 20

Note: you can easily visualise your working with a table. That will save time on test day.

You can also memorise a DST “triangle” that will help you remember the relationship between speed, distance and time. You’ll know how to rearrange the formula to find any one of those without having to think about it.

The Ultimate GRE Cheat Sheet has a great chapter on Speed, Distance, Time as well as other topics like mixtures and rates that share some time saving techniques.

Go to Ultimate Tuition to find out more!