A car traveled from Town A to Town B. The car traveled the first of th

Question

A car traveled from Town A to Town B. The car traveled the first 3/8 of the distance from Town A to Town B at an average speed of x miles per hour, where x > 0. The car traveled the remaining distance at an average speed of y miles per hour, where y > 0. The car traveled the entire distance from Town A to Town B at an average speed of z miles per hour. Which of the following equations gives y in terms of x and z ?

A. \(y = \frac{3x + 5z}{8}\)

B. \(y = \frac{3x - 5z}{8}\)

C. \(y = \frac{8x - 3z}{8}\)

D. \(y = \frac{8x - z}{5xz}\)

E. \(y = \frac{5xz}{8x - 3z}\)

A.  y = \frac{3x + 5z}{8}

B.  y = \frac{3x - 5z}{8}

C.  y = \frac{8x - 3z}{8}

D.  y = \frac{8x - z}{5xz}

E.  y = \frac{5xz}{8x - 3z}

Harshjha001 · Answer

i am getting 3xz / (8x - 5z).

Can somebody explain ?

rohitagr999 · Answer

i am too getting same answer. Please someone explain

Bunuel · Answer

______________________
Fixed the typo. Thank you!

Fdambro294 · Answer

Average Speed of the Entire Journey = (Total Distance Traveled) / (Total Time of the Journey)

becomes:

Total Time of the Journey = (Total Distance Traveled) / (Average Speed of the Entire Journey)

Let the Total Distance = D

and we are Given that the Average Speed = Z

then:

Total Time of the Journey = D/Z = (Time 1) + (Time 2) ---- (eq I)

where Time 1 and Time 2 = the Time to complete each part of the journey

and Time = (Distance covered) / (Speed)

Part 1 of Journey:

Travels 3/8th of the Distance at a Speed of X

Time 1 = (3/8)*D ---- Divided by Speed of X -----> (3D) / (8X)

Part 2 of Journey:

Travels the Remaining Distance (5/8th of the Distance) at a Speed of Y

Time 2 = (5D) / (8Y)

Plug each Time into (eq I)

Time to complete Journey = (Time 1) + Time 2)

(D/Z) = (3D / 8X) + (5D / 8Y)

---Cancel the Variable D in the NUM of each Term and then Isolate the Term with Variable Y in the DEN--

(1/Z) - (3 / 8X) = (5 / 8Y)

----Combine the Terms on the left hand side of the Equation----

(8X - 3Z) / (8XZ) = (5 / 8Y) = (5/8) * (1/Y)

----Multiply both Sides of the equation by (8/5) ---- the 8 will cancel with the 8 in the DEN on the left hand side----

(8X - 3Z) / (5XZ) = (1/Y)

----now take the Reciprocal of both sides of the Equation----

(5XZ) / (8X - 3Z) = Y

Answer:

(5XZ) / (8X - 3Z)

E

Introvertuprising · Answer

Take the Distance D=80

3/8 distance covered in x=30 miles/hr 
 
3/8*80 =30/30 =1

Remaining distance at y=50 miles/hr

50/50 =1

Avg speed =Total Distance/Total time = 80/2 =40(z)

5xz/8x-3y =5*30*40 /(8*30) - (3*40)

6000/240-120 =6000/120 =50

Ans E

A car traveled from Town A to Town B. The car traveled the first of th

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

A car traveled from Town A to Town B. The car traveled the first of th

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards