Problem Solving

Richard began driving from home on a trip averaging 30 miles per hour. How many miles per hour must Carla drive on average to catch up to him in exactly 3 hours if she leaves 30 minutes after Richard?

- 35
- 55
- 39
- 40
- 60

.A

distance driven by R = 30 * 3hours = 90 miles
C has to drive 90 miles in 2.5 hours to catch upto R.
90 = Rate * 2.5 ;
Rate = 36.

Hey thanks for your reply! If you don't mind can you explain from where did you get the 2.5 hours?
Also 36 isn't one of the given answers? Should we approximate or what?

Carla left 30 minutes after Richard. Richard is traveling 30 miles per hour. That means when Carla started Richard was 15 miles ahead of her. Carla needs to drive at a speed that will allow her to make up those fifteen miles in three hours. To travel 15 miles in three hours would require a rate of 5 mph. But remember Richard is still traveling at 30 mph so you have to add the 5 mph to Richard's speed of 30 mph. Thus, the answer is 35 mph. Hope this helps...

vijaynaik wrote:.A

distance driven by R = 30 * 3hours = 90 miles
C has to drive 90 miles in 2.5 hours to catch upto R.
90 = Rate * 2.5 ;
Rate = 36.

This problem can also be solved this by this method. Carla drives for exactly 3 hours. Richard drives for an additional 30 minutes, so his total time is 3.5 hours. Richard drives at 30 mph so his total distance is 105 miles. Carla needs to drive 105 miles in 3 hours or 35 mph.

All of these problems use some form of the equation: Distance = Rate X Time

Yep thanks for explaining mate. I had a problem understanding the wording in the problem but it's clear now.
thanks again
Have a great day

N:Dure wrote:Richard began driving from home on a trip averaging 30 miles per hour. How many miles per hour must Carla drive on average to catch up to him in exactly 3 hours if she leaves 30 minutes after Richard?

- 35
- 55
- 39
- 40
- 60

The method of Relative Speed works best here:

In 30 mins, Richard has covered = 15 miles... So, now Carla needs to cover 15miles in 3 hours...

Hence use the simple D = R * T,

-> 15/(x-30)=3... we use x-30 coz they are travelling in the same direction...

solve x = 35...

Hope it Helped

N:Dure wrote:Richard began driving from home on a trip averaging 30 miles per hour. How many miles per hour must Carla drive on average to catch up to him in exactly 3 hours if she leaves 30 minutes after Richard?

- 35
- 55
- 39
- 40
- 60

I find the easiest way to deal with these kinds of problems is to set up R X T = D tables.

RATE (m/hr) X TIME (Hrs) = DISTANCE
Richard 30 X 3.5 = 105
Carla ?? X 3.0 = 105

The distance for R and C should be idential at 105m. We need to solve for Carla's speed i.e., ??
Carla will catch Richard in 3 hours (105m) if she travels at 105/3.0 = 35m/hr

Therefore the correct answer is A = 35

N:Dure wrote:Richard began driving from home on a trip averaging 30 miles per hour. How many miles per hour must Carla drive on average to catch up to him in exactly 3 hours if she leaves 30 minutes after Richard?

- 35
- 55
- 39
- 40
- 60

Richard: Rate: 30mph; Time: 3.5 (since we have 3 hours + 30 minutes); Distance: 30*3.5
Carla: Rate: R; Time: 3 (since she left 30 minutes after Richard); Distance: 3R

We want Carla to catch up to Richard, so we need to find out how fast Carla needs to travel to equal the distance Richard has traveled. So, Carla = Richard

30(3.5) = 3R
105 = 3R
R = 35

in 30 min Rich covers = 15 miles
So in 3 hrs Carla has to cover 15 miles extra i.e. 5 miles every hr.
So her speed should be 30 + 5 =35 hence A.

N:Dure wrote:Richard began driving from home on a trip averaging 30 miles per hour. How many miles per hour must Carla drive on average to catch up to him in exactly 3 hours if she leaves 30 minutes after Richard?

- 35
- 55
- 39
- 40
- 60

in 3.5 hrs richard drove 105 miles
to catch up, 105/3 = 35 m/hr

IMO A

I like to look at this one from a slightly different perspective.

Richard left 30 mins before Carla so will have travelled for 3.5 hours when they meet.
3.5hrs x 30 miles an hour = 105 miles covered

Carla must travel 105 miles in 3 hours to catch Richard.

105/3hrs = 35mph

"catch up" means, that C and R drove the same distance when they met.
So, we have
3*x=30*(3+1/2) (1/2 is 30min/60 min=1/2 h)
x=35

C's speed is 35

If x miles/hr is speed, x*(3) = 30*(3+1/2) => x = 35