James left the hardware store and traveled toward the capital at an average speed of 28 km/h. Some time later Julio left traveling in the same direction but at an average speed of 35 km/h. After traveling for four hours Julio caught up with James.

## How long did James travel before Julio caught up with him?

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# 4 Answers

distance=rate x time

distances are the same

let t=James's time

28*t=35*4

28t=140

t=140/28=5 hours

The distance James traveled = the catch up distance by Julio = (35-28)*4 = 28 km

So, James traveled 28/28 + 4 = 5 hours before Julio caught up with him.

Julio: (35 km/hr)*(4 hr) = 140 km

James (28 km/hr)*t = 140 km

t = (140 km)/(28 km/hr) =

**5 hours**Hi Samantha;

James=28 km/h; (4+x) hours

Julio=35 km/h; 4 hours

Our first priority is to check for consistency of units. For example, is any information provided in minutes or miles. Everything is consistent, in kilometers and hours, so we may proceed.

We know that both men traveled the same distance when Julio caught up with James.

(28 km/hour)[(4+x)hours]=(35 km/hour)(4 hours)

Let's cancel units where appropriate...

(28 km/hour)[(4+x)hours]=(35 km/hour)(4
hours)

Let's proceed to cancel units where appropriate...

(28 km)(4+x)=(35
km)(4)

28(4+x)=35(4)

Cancelling units is always your first priority, before calculations. This is because if the units are not aligned, you are working with the wrong equation.

112+28x=140

Let's subtract 112 from both sides as we proceed to isolate x...

28x=140-112

28x=28

x=1

James traveled 1 hour + 4 hours=5 hours