Rachel and Rob live 190 miles apart. They both drive in a straight lin

Question

Rachel and Rob live 190 miles apart. They both drive in a straight line toward each other to meet for tea. If Rachel drives at 50 mph and Rob drives at 70 mph, then how many miles apart will they be exactly 45 minutes before they meet?

A. 50
B. 60
C. 70
D. 90
E. 100

A. 50
B. 60
C. 70
D. 90
E. 100

GMATMBA5 · Accepted Answer

IMO D.

D = 190
Relative speed S = 70+50=120
Time when Rachel and Rob meet T = 190/120= 19/12 hours

45 minutes before they meet can be represented as, T - 3/4 hours = 19/12 - 3/4 = 5/6 hours

distance covered by Rachel 45 min before she meets Rob = 50*5/6
distance covered by Rob 45 min before he meets Rachel = 70*5/6
Total distance covered by Rachel and Rob when they meet each other = 50*5/6 + 70*5/6 = 5/6*120 = 100 miles

So Rachel and Rob will be 190-100= 90 miles apart 45 mins before they meet.

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 Kudos if helpful!

Archit3110 · Answer

total relative speed = 50+70 = 120 mph
distance = 190 miles
so total time they would take = 190/120 = 1.58 hours
45 mins = 45/60 = 0.75 hrs 
so before 0.75 hrs they both have travelled for 1.58-0.75 = 0.83 hrs
distance travelled by Rachel = 0.83 * 50 = 41.5 miles and rob = 0.83 * 70 = 58.1
total distance = 99.6 ~100 miles
so they are 190-100 = 90 miles apart
IMO D

ScottTargetTestPrep · Answer

We can let t = the time if takes to meet and create the equation:

50t + 70t = 190

120t = 190

t = 190/120 = 19/12 hours or 19/12 x 60 = 95 minutes

So each will have driven for 50 minutes when it is 45 minutes before they meet. Therefore, together they will have driven (50 + 70) x 50/60 = 120 x 50/60 = 2 x 50 = 100 miles. Since the total distance is 190 miles, they will be 190 - 100 = 90 miles apart when it is exactly 45 minutes before they meet.

Alternate solution:

Notice that the distance between the two decreases by 50 + 70 = 120 miles every hour. Since they have to drive 45 more minutes to meet when it is exactly 45 minutes before they meet, they must be (50 + 70) x 45/60 = 120 x 45/60 = 2 x 45 = 90 miles apart.

Answer: D

hellosanthosh2k2 · Answer

Let X be meeting point.
Rob------------------------------------X-------------------------------------------Rachel

45 mins prior to meeting point, Rachel would have travelled (3/4 * 50) miles from right of X to X
and Rob would have travelled (3/4 * 70) miles from left of X to X.

so distance apart = (3/4) * 50 + (3/4) * 70 = (3/4) * 120 = 90 miles

ahnaf128 · Answer

total speed = 70+50 mph ( as they are moving towards each other)
total distance = 190 miles
they are covering 120 miles in 1hr
so the remaining miles to cover is 190-120 = 70 miles
time taken to cover 70 miles is t = 70/120*60 = 35 mins (*60 for minute conversion)
it's evident that they are covering 2 miles per minute hence 45*2 = 90 miles

devdattakhoche · Answer

Let  d  be the distance between Rachel and Rob, which is initially  190  miles.
Rachel drives at a speed of  50  mph and Rob drives at a speed of  70  mph.
Since they are driving towards each other, their relative speed is the sum of their speeds:
 50 + 70 = 120  mph.

Let  t  be the time in hours until they meet. Then,

120t = 190

t = \frac{190}{120} = \frac{19}{12}  hours.

We want to find the distance between them 45 minutes before they meet.
45 minutes is  \frac{45}{60} = \frac{3}{4}  hours.
So we want to find the distance between them at time
 t - \frac{3}{4} = \frac{19}{12} - \frac{3}{4} = \frac{19}{12} - \frac{9}{12} = \frac{10}{12} = \frac{5}{6}  hours.
In  \frac{5}{6}  hours, Rachel travels
 50 \cdot \frac{5}{6} = \frac{250}{6} = \frac{125}{3}  miles.
In  \frac{5}{6}  hours, Rob travels
 70 \cdot \frac{5}{6} = \frac{350}{6} = \frac{175}{3}  miles.
The total distance they have traveled is
 \frac{125}{3} + \frac{175}{3} = \frac{300}{3} = 100  miles.
Therefore, the distance between them at that time is
 190 - 100 = 90  miles.

Final Answer:  The final answer is  \boxed{90}

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