Speed, distance, time problem

[Mathuserr]

Help me solve please!

To get to the camp in time, tourists had to go with a speed 4km/h. They went with that speed half of the road, but then they drove with a bus and arrived to the camp 2h 20min earlier, before the planned time. How many kilometers did tourists drive with the bus, if the speed of the bus was 60km/h?
Hint: make "x" the distance tourists had to travel.

 

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[Otis]

Hi Mathuserr. I'd start by sketching a diagram, to organize the given info. The time difference between walking the second half versus riding the bus is 7/3 hours, right?

I would label each half of distance x with expressions for time (that's distance/rate). You could use subscripted variables to name them.

t₁ = time walking first half

t₂ =time riding second half

Your expressions for the two times will be in terms of x.

If they had also walked the second half, then that longer time would have been the same as t₁. But they rode the bus for t₂ hours, instead. The difference between what the time would have been (during the second half of the trip) and what it actually was is 7/3.

If you get stuck, please share how far you got. Thanks!

 

[JayJay]

Hi Mathuserr. I'd start by sketching a diagram, to organize the given info. The time difference between walking the second half versus riding the bus is 8/3 hours, right?

No, wrong I'm afraid. It's 2 hours and 20 minutes.

 

[Steven G]

8/3 hrs = 2 1/3 hr = 2hrs + 1/3hr = 2hrs + 20 minutes. I guess Otis was correct!

 

[JayJay]

Are you saying:

2 hrs and 20 minutes is NOT equal to 8/3 hours?

Yes, I am.

 

[Steven G]

So where did I make my mistake in post #5 where I claim that I showed that 8/3 hrs = 2hr + 20 minutes?

 

[skeeter]

8/3 hr = 2 2/3 hr = 2 hrs 40 min

7/3 hr = 2 1/3 hr = 2 hrs 20 min

 

[Otis]

No, wrong I'm afraid. It's 2 hours and 20 minutes.

I regret my typo, JayJay. Thanks for pointing it out. The time difference is 7/3 hours.

@Mathuserr: Did you understand the rest of my post? Can you show some work?

 

[Otis]

So where did I make my mistake in post #5 where I claim that I showed that 8/3 hrs = 2hr + 20 minutes?

My goof was a typo (this time), but I'm headed to the sub-basement, anyway. See you in the corner!

?

 

[Deleted member 4993]

Yes, I am.

Good thing you know that - I wanted Jomo & Otis to see that fix the typo. I had deleted my post - figuring that will create more Khan-fusion.

 

[Deleted member 4993]

I regret my typo, JayJay. Thanks for pointing it out. The time difference is 7/3 hours.

Did you understand the rest of my post? Can you show some work?

JayJay is not the OP. By the way - the OP did not show a line of "original" work!!