Can someone please help with this math question?

Suppose the original trip took t hours. The distance traveled at 50 km/h was 50t km. You're told that the return trip took 15 min. (0.25 h) longer traveling at 50+6 = 56 km/h, That's a return distance of 56(6 + 0.25) km; and that this distance is 26 km longer than the original. So:

56(t + 0.25) = 50t + 23

56t + 14 = 50t + 23

6t = 23 - 14 = 9

t = 9/6 = 1.5 h

That's the original driving time. The return trip was 0.25 hr longer:

t + 0.25 = 1.75 h

That's an hour and 45 minutes, or 105 minutes if you prefer.

Distance:

d1 is distance he drove to friend's house

d2 is distance he drove back

Speed:

v1 = speed to friend's house

v2 = speed from friend's house

Time:

t1 = d1/v1

t2 = d2/v2

Things we know:

d1 = d2 - 23km

v1 = 50km/h

v2 = 56km/h

t1 = t2 - 0.25h (15min = 0.25h)

Use this equation

v1 = d1/t1

where

d1 = d2 - 23km

t1 = t2 - 0.25km = d2/v2 - 0.25h

v1 = (d2 - 23km)/(d2/v2 - 0.25h)

Multiply by d2/v2 - 0.25h

v1/v2 *d2 - 0.25h*v1 = d2 - 23km

Plug in known values for v1 and v2

50/56 d2 - 12.5km = d2 - 23km

Multiply by 56

50d2 - 700km = 56d2 - 1288km

588km = 6d2

d2 = 98km

d1 = d2 - 23km

d1 = 98km - 23km

d1 = 75km

t1 = d1/v1

t1 = 75km/50km/h

t1 = 1.5h

Recall: s = d/t → where s is the speed, d is the distance, t is the time

On the way to his friend's house, Latif drives at an average speed of 50 km/h.

s₁ = d₁/t₁ → where: s₁ = 50 km/h

50 = d₁/t₁

50.t₁ = d₁

When he returns home, Latif takes a longer route that has better roads.

s₂ = d₂/t₂ → he drives an extra 23 km, so: d₂ = d₁ + 23

s₂ = (d₁ + 23)/t₂ → his average speed is 6 km/h higher, so: s₂ = s₁ + 6 = 56

56 = (d₁ + 23)/t₂ → the journey takes him an extra 15 min, i.e. 0.25 h, → t₂ = t₁ + 0.25

56 = (d₁ + 23)/(t₁ + 0.25)

56.(t₁ + 0.25) = d₁ + 23 → recall: d₁ = 50.t₁

56.(t₁ + 0.25) = 50.t₁ + 23

56.t₁ + 14 = 50.t₁ + 23

56.t₁ - 50.t₁ = 23 - 14

6.t₁ = 9

t₁ = 9/6

t₁ = 1.5 hours

t₁ = 1 h + 0.5 h

t₁ = 1 h + 30 min ← to go to his friend's house

Recall:

t₂ = t₁ + 15 min

t₂ = 1 h + 30 min + 15min

t₂ = 1 h + 45 min ← to return home