The Schoolboy's Route
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Exercise:
Each morning Boris walks to school. At onfourth of the way he passes the machine and tractor station; at onthird of the way the railroad station. At the machine and tractor station its clock shows : and at the railroad station its clock shows :. When does Boris leave his house when does he reach school?
Solution:
Between : and : al Delta t tau_ - tau_ hmin - hmin min s are passing. This corresponds to al Deltaeta eta_ - eta_ frac - frac frac of the time for the whole way i.e. the whole way takes al t fracDelta tDelta eta fractau_-tau_eta_-eta_ fracsfrac s .h. One third of this time is al t_ eta_ t fraceta_eta_-eta_ qtytau_-tau_ fracs s min. Thus he leaves the house at al ssctauleave tau_ - t_ tau_ - fraceta_eta_-eta_ qtytau_-tau_ hmin - min hmin rightarrow text:. From the gas station to school it takes him al t_ -eta_ t frac-eta_eta_-eta_ qtytau_-tau_ qty-frac s s min and he therefore reaches school at al ssctaureach tau_ + t_ tau_ + frac-eta_eta_-eta_ qtytau_-tau_ hmin + min hmin rightarrow text:. Less formal solution: From onfourth to onthird its ontwelfth: frac-fracfrac For this part of the way the boy Boris needs minutes; his whole route to school is minutes long. He starts at : at home goes fracfrac of the way is at : at the machine and tractor station : at the railroad station where fracfrac of the way are still remaining which takes him another minutes; he arreives at :.
Each morning Boris walks to school. At onfourth of the way he passes the machine and tractor station; at onthird of the way the railroad station. At the machine and tractor station its clock shows : and at the railroad station its clock shows :. When does Boris leave his house when does he reach school?
Solution:
Between : and : al Delta t tau_ - tau_ hmin - hmin min s are passing. This corresponds to al Deltaeta eta_ - eta_ frac - frac frac of the time for the whole way i.e. the whole way takes al t fracDelta tDelta eta fractau_-tau_eta_-eta_ fracsfrac s .h. One third of this time is al t_ eta_ t fraceta_eta_-eta_ qtytau_-tau_ fracs s min. Thus he leaves the house at al ssctauleave tau_ - t_ tau_ - fraceta_eta_-eta_ qtytau_-tau_ hmin - min hmin rightarrow text:. From the gas station to school it takes him al t_ -eta_ t frac-eta_eta_-eta_ qtytau_-tau_ qty-frac s s min and he therefore reaches school at al ssctaureach tau_ + t_ tau_ + frac-eta_eta_-eta_ qtytau_-tau_ hmin + min hmin rightarrow text:. Less formal solution: From onfourth to onthird its ontwelfth: frac-fracfrac For this part of the way the boy Boris needs minutes; his whole route to school is minutes long. He starts at : at home goes fracfrac of the way is at : at the machine and tractor station : at the railroad station where fracfrac of the way are still remaining which takes him another minutes; he arreives at :.