movement Problems: “Catch Up”

Motion problems are among the most typical word problems you’ll conference on the Quantitative ar of the GMAT. These trouble solving questions loss into one of three categories:

Motion in the same Direction (“Catch Up” Problems)

In this great we’ll cover motion in the same Direction.

You are watching: Two objects moving in the same direction at different speeds

2. Activity in the same Direction (“Catch Up”): The Basics

All varieties of activity questions top top the GMAT require you to use the following basic Distance Formula:

Distance = rate * Time

The basic idea with very same Direction — or “Catch Up” — activity questions is the you have actually two entities relocating in the same direction at different rates the speed. One entity generally starts ~ the various other entity and also travels in ~ a much faster rate of rate to “catch up” through the first entity. The inquiry itself will normally ask girlfriend to figure out how long that takes because that the second entity to record up with the very first entity, or perhaps how much street the second entity need to travel before overtaking (i.e. “catching up with”) the very first entity.

Regardless the what details is offered to you and what you’re ultimately asked to resolve for, this questions constantly come down to solving for one of the variables in the street Formula. There room three critical steps to finding the missing piece the the inquiry is asking you to resolve for.

The Strategy

Step 1: Draw a diagram illustrating what the difficulty is informing you. This will assist you visualize what you’re solving for and also get her mind about the inquiry itself.

The chart will usually look something prefer this:


Step 2: The best starting point for solving exact same Direction concerns is to usage this formula:

d = d₂

Step 3: set up one individual distance formula because that each entity, d₁ and also d₂, and set them equal to each other.* You might be inquiry to discover the distance traveled by every entity, or possibly you’ll just be asked how long (i.e. time in the distance Formula) it takes one entity to record the other.

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* Note: On harder questions, Person/Entity 2 might start from additional away or overtake Person/Entity 2 by a certain distance. In that case, obviously d₁ and d₂ will not it is in equal. You’ll desire to use your diagram as a overview and readjust your equation as necessary. For example, if the trouble asks you exactly how long it will certainly take because that Person/Entity 2 come catch and also overtake Person/Entity 1 through 2 miles, then her diagram might look like this:


Thus, because that those two distances to be “equal,” you’ll have actually to change your equation as follows (assuming the rate is provided in miles):

d + 2 = d₂

In other words, Person/Entity 1 would certainly in theory need to travel an additional 2 mile in order for his distance to same Person/Entity 2’s distance.

On the GMAT

This will certainly all make more sense as soon as you see how this strategy is applied to a sample GMAT question. Clock this video clip for a step-by-step application: