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Two trucks are parked at Lucy's Diner. Chuck takes off, at 50 miles pe

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Two trucks are parked at Lucy's Diner. Chuck takes off, at 50 miles pe  [#permalink]

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28 Apr 2017, 11:01
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Difficulty:

45% (medium)

Question Stats:

67% (01:49) correct 33% (02:09) wrong based on 128 sessions

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Two trucks are parked at Lucy's Diner. Chuck takes off, at 50 miles per hour, heading due east at 9 a.m. in one of the trucks. Two hours later Patricia takes off, at 70 miles per hour, in the other truck heading due west. How long from Chuck's departure time will it be until they are 700 miles apart?

A. 3 hrs. 11 minutes
B. 5 hrs.
C. 5 hrs. 50 minutes
D. 7 hrs.
E. 11 hrs. 40 minutes

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Re: Two trucks are parked at Lucy's Diner. Chuck takes off, at 50 miles pe  [#permalink]

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28 Apr 2017, 11:11
Chuck at 2 hours would have traveled 100 miles.

After Patricia starts driving,
Chuck and Patricia drive at their speeds 50 miles/hr and 70 miles/hr. As they are moving in the opposite direction, their net speed is 120 miles/hr.

They need to travel another 600 miles to be 700 miles apart as they are travelling in the opposite direction. This will take them another 5hours(600 miles/120 miles/hour)

So time taken from Chuck's departure time is 7 hours(Option D)

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Two trucks are parked at Lucy's Diner. Chuck takes off, at 50 miles pe  [#permalink]

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28 Apr 2017, 11:58
You can also do process elimination for this.
Let's look at D

First work out how many miles Chuch drove within 2 hrs
50 x 2 = 100

Then multiply 500 by 5 then add it by 100
(500 x 5) + 100 = 350 miles

Patricia drove
70 x 5 = 350 miles

350 + 350 = 700 miles apart

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Re: Two trucks are parked at Lucy's Diner. Chuck takes off, at 50 miles pe  [#permalink]

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29 Apr 2017, 16:25
Must be D. Chuck drives for 2 hours (100) and then 70 + 50 = 120 * 5 = (600).

7 hours in total.

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Re: Two trucks are parked at Lucy's Diner. Chuck takes off, at 50 miles pe  [#permalink]

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02 May 2017, 00:34
chuck leaves early,,,in 2 hours he completes 100 miles

hence 600 more miles to be covered,,

relative speed = 120mph

600/120 = 5 hrs

total 5 hrs + 2 hrs = 7 hrs...

ans D
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Two trucks are parked at Lucy's Diner. Chuck takes off, at 50 miles pe  [#permalink]

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02 May 2017, 13:01
Bunuel wrote:
Two trucks are parked at Lucy's Diner. Chuck takes off, at 50 miles per hour, heading due east at 9 a.m. in one of the trucks. Two hours later Patricia takes off, at 70 miles per hour, in the other truck heading due west. How long from Chuck's departure time will it be until they are 700 miles apart?

A. 3 hrs. 11 minutes
B. 5 hrs.
C. 5 hrs. 50 minutes
D. 7 hrs.
E. 11 hrs. 40 minutes

let t=time both are driving
2*50+120t=700 miles
t=5 hrs
t+2=7 hrs
D
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Re: Two trucks are parked at Lucy's Diner. Chuck takes off, at 50 miles pe  [#permalink]

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02 May 2017, 14:06
In first 2 hours Chuck travels 50*2=100miles
So the remaining distance =600 miles
Now both the trucks are moving away at a speed of 50+70=120 miles per hour
So the time taken to increase the distance to 600 miles will be =600/120=5 hrs
Hence the total time will be 5+2=7 hrs option d

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Re: Two trucks are parked at Lucy's Diner. Chuck takes off, at 50 miles pe  [#permalink]

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10 May 2017, 11:32
1
Bunuel wrote:
Two trucks are parked at Lucy's Diner. Chuck takes off, at 50 miles per hour, heading due east at 9 a.m. in one of the trucks. Two hours later Patricia takes off, at 70 miles per hour, in the other truck heading due west. How long from Chuck's departure time will it be until they are 700 miles apart?

A. 3 hrs. 11 minutes
B. 5 hrs.
C. 5 hrs. 50 minutes
D. 7 hrs.
E. 11 hrs. 40 minutes

We can use the following formula:

Distance of Chuck + distance of Patricia = total distance between the trucks

We are given that Chuck leaves the diner at 9 a.m. traveling at a rate of 50 mph and Patricia leaves at 11 a.m. traveling at a rate of 70 mph. We can let Chuck’s time = t + 2 and Patricia’s time = t. Thus, the distance for Chuck is 50(t + 2) = 50t + 100 and the distance for Patricia = 70t. Finally, we have:

50t + 100 + 70t = 700

120t = 600

t = 5

Since Chuck traveled for t + 2 hours, the two trucks were 700 miles apart when Chuck had been driving for 7 hours.

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Re: Two trucks are parked at Lucy's Diner. Chuck takes off, at 50 miles pe &nbs [#permalink] 10 May 2017, 11:32
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